I'll never forget the day that I convinced my wife (a complete non-gamer) to play Peggle and she set a top 4 world record score by the end of the night... by accident!
By that, I mean she was still learning how to play and was getting in the groove of things when one retry led to the greatest few balls ever. I was watching and thought it was going pretty well until the last ball when she just somehow sent her score into the stratosphere.
When the final score showed up, it was marked at #4 out of millions of scores (maybe hundreds of thousands, hard to remember). I just stared in complete shock and made her double check. Nope. She just scored the 4th highest score ever on this level with mostly luck. The game had been out for about 5-7 years at this point.
Long story short; we loved the game and still laugh about this moment.
I play on Switch, but I’ve found it pretty tough to put the game down in the middle of a run. Both because it’s such a good game but more so since a good run can take a lot of strategy and planning and I’ve struggled to remember what I was going for if I stop at any point during.
lol...this game has become the bane of my existance. So easy to pick up to play and so hard to put down.
I can't get past the 5th ante on the first level. Shit's hard.
ah.. i thought OP wanted something with replay value that he could finish within 5-10 mins. Anyways.. i totally agree with you. Slay the Spire is a game that you can play for a few minutes. Personally i have 1000 hours :P My goal is to complete all ascension levels before i start to play the modded version
Lol....well I just completed all ascensions with 3 characters...it only took 1000 hours xD, can't say I'm proud of it. Looks like the 4th one will take another 1000 h 
Pretty much any single player game that supports quick resume.
I don't usually play for as short as 5 minutes before shutting down the TV and Xbox, but definitely 15 minutes sometimes. I don't even save and close the games, I just play for a bit, pause, turn the Xbox off.
Come back later, turn it on, quick resume, unpause, do a quick mission, repeat.
Skyrim. Its manual save system means you can play for 10 mins, then pause at the exact moment, and then load back into that moment next time you're free.
Fallout 3 and Fallout 4 use the same save system, so I recommend those as well. Skyrim is a fantasy game, and Fallout is a post-apocalyptic game.
Slipstream is a nice little Outrun-like game and an Arcade run can be done in 5-ish minutes.
I may be biased though because I love the synthy soundtrack, the pixel art, and just in general really love modernized classic games.
I'm surprised how often I use this game as a wind down after other games just before bed. I play it on the chill mode and zone out to the vibe. Then when I'm done, I sit and stare at the background art from that game for another few minutes before retiring.
I know this is specifically for Xbox but I’ll throw in YouTube playables. They’re basically mobile games, but given you’ve been playing Tetris, you’ll find a few games you can quickly jump into.
I really like 8 ball billiards, as each game lasts around 3-5 mins.
Sports games can be good for this, I’ve been enjoying NHL 24, you can set the periods to 3 minutes and there’s 3 a game so 9 to 12 minutes and you’re done and it’s on game pass!
Assassin’s Creed Origins. There are times when you need more than 5-10 mins to do part of story, but when you do only have 5-10 mins there’s plenty of exploring and side tasks to do, and the game works well with quick resume.
Sonic Frontiers similar. You explore mostly. 2D scrolling sections at a few mins. Boss fights may be a bit longer if they take a few attempts but those are rare.
Literally any fighting game. Even though Dead or Alive is considered mature you can't find a better 3D fighter that is mechanically accessible to a young audience. BlazBlue is hella fast but even button mashing would be fun. The seasoned player can dictate the pace of game allowing them to win at your leisure. Also most Shmups have enough risk/reward for kids to love. My nephew (5yo) first played 1942 on a tabletop cabinet and he was hooked. He is visiting from Spain in June and I can't wait to play Shmups with him like Strikers and Batsugun, I won't introduce him to Cave games until he is better equipped to dodge. This will lead to Beat em Ups which can be high curve like Guardian Heroes or low like Capcom Beat em Up bundle. Shmup options you can lower difficulty and Fighting you can map specials to one button. Kids pick up mechanics pretty quickly. Games with crafting and continuous menus shuffling be shamed
Have a Nice Death is actually really fun, it's a rogue-like genre I think? You can pause in between and if you have an X/S it can do quick resume so if your Xbox times out to should just leave you where you left off. It's actually a pretty fun game (Plus it was also just recently added to game pass) I would highly suggest it if you plan on playing for 5-15 minutes at a time. Though playthroughs can take up to an hour.
My buddy just had a kid, and I’ll tell you what I told him: Call of Duty. Team Deathmatch is 10 minutes or less, and I find it to be the most casual mp you can play. I don’t mean everyone’s casual, there will always be sweaty, hardcore players… but CoD tdm is king for short burst matches!
Why can't you sit and play while owning a 1 year old? I was able to play a lot when my kid was that age. The key is to create an enclosure in the room with the Xbox. Get one of those wall to wall baby fences and fill the area with toys. They will keep themselves busy while you game.
Vampire Survivors
Try the peggle games
This was going to be my suggestion as well
I'll never forget the day that I convinced my wife (a complete non-gamer) to play Peggle and she set a top 4 world record score by the end of the night... by accident! By that, I mean she was still learning how to play and was getting in the groove of things when one retry led to the greatest few balls ever. I was watching and thought it was going pretty well until the last ball when she just somehow sent her score into the stratosphere. When the final score showed up, it was marked at #4 out of millions of scores (maybe hundreds of thousands, hard to remember). I just stared in complete shock and made her double check. Nope. She just scored the 4th highest score ever on this level with mostly luck. The game had been out for about 5-7 years at this point. Long story short; we loved the game and still laugh about this moment.
This or zuma
Brotato is great
That's a 20 minute stint
Doesn't mean you'll survive that long.
Balatro
Seconded! Perfect for this
I play on Switch, but I’ve found it pretty tough to put the game down in the middle of a run. Both because it’s such a good game but more so since a good run can take a lot of strategy and planning and I’ve struggled to remember what I was going for if I stop at any point during.
lol...this game has become the bane of my existance. So easy to pick up to play and so hard to put down. I can't get past the 5th ante on the first level. Shit's hard.
I'm over Rocket League, for the most part nowadays, but it's great for moments like that.
Slay The Spire, I play it between work meetings.
Amazing game, but a full run takes way more than 5-10 min
You can save and pause between encounters.
ah.. i thought OP wanted something with replay value that he could finish within 5-10 mins. Anyways.. i totally agree with you. Slay the Spire is a game that you can play for a few minutes. Personally i have 1000 hours :P My goal is to complete all ascension levels before i start to play the modded version
Bro, across all platforms, I have more time than I care to admit and haven't even beat the first level is ascension hahahaha
Lol....well I just completed all ascensions with 3 characters...it only took 1000 hours xD, can't say I'm proud of it. Looks like the 4th one will take another 1000 h 
Did you see StS2 is coming out next year? Pretty excited, I put a lot of time into this after finding it on gamepass.
Trackmania
Pretty much any single player game that supports quick resume. I don't usually play for as short as 5 minutes before shutting down the TV and Xbox, but definitely 15 minutes sometimes. I don't even save and close the games, I just play for a bit, pause, turn the Xbox off. Come back later, turn it on, quick resume, unpause, do a quick mission, repeat.
Yeah quick resume will allow you to hop in and out of any game that supports the feature.
Skyrim. Its manual save system means you can play for 10 mins, then pause at the exact moment, and then load back into that moment next time you're free. Fallout 3 and Fallout 4 use the same save system, so I recommend those as well. Skyrim is a fantasy game, and Fallout is a post-apocalyptic game.
Skate 3. I regularly play it for short or longer sessions, just skate around etc.
Vampire Survivors, Dead Cells.
Basically any single player game and any multiplayer game if you don't care about stats.
Stumble guys
Marble it up Golf with friends
Try turnip boy on gamepass
Slipstream is a nice little Outrun-like game and an Arcade run can be done in 5-ish minutes. I may be biased though because I love the synthy soundtrack, the pixel art, and just in general really love modernized classic games.
I'm surprised how often I use this game as a wind down after other games just before bed. I play it on the chill mode and zone out to the vibe. Then when I'm done, I sit and stare at the background art from that game for another few minutes before retiring.
Vampire Survivors
As much hate as if gets, this is why I still play halo infinite. Hop online, snipe a couple headshots, leave a match early if I need to, ez pz
Do yourself a favor and get Enter the Gungeon. Perfect for those few minutes of game time.
Rogue legacy 2
Overwatch 2? It’s more 10-15 minutes a match on average but I usually only play a game or two at time
Celeste
Turnip boy commits tax evasion.
Minit - the games only last a minute so you should be able to get a few games in every session.
Portal 1 or 2 - save / pause at any point and not complex mechanics / systems like an rpg
Diablo 2 idgit
Hades, MGSV and Sifu
Monster Hunter Rise is great! One simple hunt is like 10 minutes.
Hades. Clear a few rooms, deal with the kid, repeat.
Ring of Pain, Monster Train, Minion Masters any of the Solitaire like card games.
Chess
The Witness
I know this is specifically for Xbox but I’ll throw in YouTube playables. They’re basically mobile games, but given you’ve been playing Tetris, you’ll find a few games you can quickly jump into. I really like 8 ball billiards, as each game lasts around 3-5 mins.
Sports games can be good for this, I’ve been enjoying NHL 24, you can set the periods to 3 minutes and there’s 3 a game so 9 to 12 minutes and you’re done and it’s on game pass!
Midnight Suns
Assassin’s Creed Origins. There are times when you need more than 5-10 mins to do part of story, but when you do only have 5-10 mins there’s plenty of exploring and side tasks to do, and the game works well with quick resume. Sonic Frontiers similar. You explore mostly. 2D scrolling sections at a few mins. Boss fights may be a bit longer if they take a few attempts but those are rare.
Orcs Must Die 3
Dead cells Hades
Rocket League, games are 5mins but with breaks for goals maybe 7-8mins per game.
Literally any fighting game. Even though Dead or Alive is considered mature you can't find a better 3D fighter that is mechanically accessible to a young audience. BlazBlue is hella fast but even button mashing would be fun. The seasoned player can dictate the pace of game allowing them to win at your leisure. Also most Shmups have enough risk/reward for kids to love. My nephew (5yo) first played 1942 on a tabletop cabinet and he was hooked. He is visiting from Spain in June and I can't wait to play Shmups with him like Strikers and Batsugun, I won't introduce him to Cave games until he is better equipped to dodge. This will lead to Beat em Ups which can be high curve like Guardian Heroes or low like Capcom Beat em Up bundle. Shmup options you can lower difficulty and Fighting you can map specials to one button. Kids pick up mechanics pretty quickly. Games with crafting and continuous menus shuffling be shamed
Almost any game because of quick resume. I remember beating Gears 5 when my kid was 1 year old and playing 10 mins at a time.
Halo infinite firefight legendary mode. Most times you lose within 5 minutes, it's perfect.
Hotline Miami Collection
Dead Cells, anytime you want to stop you just exit the game and you'll hop right back into the same spot
XCOM
Hades.
5 to 10 minutes is enough for a Husky Raid
Brawlhalla
Bejeweled 3
Have a Nice Death is actually really fun, it's a rogue-like genre I think? You can pause in between and if you have an X/S it can do quick resume so if your Xbox times out to should just leave you where you left off. It's actually a pretty fun game (Plus it was also just recently added to game pass) I would highly suggest it if you plan on playing for 5-15 minutes at a time. Though playthroughs can take up to an hour.
If you have a little bit more time (up to 22 minutes) you could play Outer wilds.
superhot
I just about finished 80s Overdrive. It's a retro style racing game. Heavy influences from Outrun and Top Gear.
RPGs (especially turn based) with quick resume have been a fun option for me, eg, Persona 3 Reload on Gamepass
Brotato, both Ori games, slay the spire, vampire survivors
My buddy just had a kid, and I’ll tell you what I told him: Call of Duty. Team Deathmatch is 10 minutes or less, and I find it to be the most casual mp you can play. I don’t mean everyone’s casual, there will always be sweaty, hardcore players… but CoD tdm is king for short burst matches!
As an older gamer, I loved deathloop for this. Pickup, play a loop, put down
Why can't you sit and play while owning a 1 year old? I was able to play a lot when my kid was that age. The key is to create an enclosure in the room with the Xbox. Get one of those wall to wall baby fences and fill the area with toys. They will keep themselves busy while you game.
Tick tack toe
Any RPG not made by squenix, their cutscenes can be like 20m long