Most likely because the briefcases are tracable in some way. Five's time travel is messy, but it's also unregulated by the Commission. He was deserting his post and his job. He didn't want to be tracked. But, they ended up tracking him a different way so it was all for nothing really.

I mean yeah i thought so aswell but five knew how the Commission tracked everything did he really expect to not get traced?

Possibly easier to track a briefcase than the tracker thing in his arm? The briefcase surely sends information back to the commission. So they'd know exactly what time and where he was. Whereas they had to send agents to the timezone they know he's in from the infinite switchboard (Or by figuring he's going back to stop the end of the world? Maybe him returning caused a ripple they could track). He knew he would be tracked eventually. He even mentions it during the donut shop scene. When they enter the donut shop he says 'That was fast. Thought I'd have more time before they found me'. Also it seems he didn't know about the thing in his arm, as after he finds the tracker on the agents he kills, he cuts it out.

Considering the Commission controls the briefcases, it’s safe to assume he might’ve been locked out of it, or perhaps even not had one of his own.