I'm about 90% sure you got stacked.

You are beaten by AA, KK, QQ, 55, 44, 33 on the flop. He raised preflop so it puts all of these in his range. If he's already entered two flops of 5 then he might be loose or just have a good run of cards. You may have run into a donk who is stupid enough to try to bluff with AK but in my experience this is rare, especially since he 4 bet you on the flop. If he's dumb enough to push with air then add him to your buddy list and keep playing against him.

I would have reraised preflop to about $1. PSB is okay on flop but then you minreraised and he pushed. If you knew you were going to push anyway why not be the one to do it?