Hmm. You push on the turn after a 5 hits and your first to act. Were you planning on pushing on the turn no matter what card came out, OR, where you representing the 5?
Analyze the texture of the flop, and put him on a range of hands when he plays back at you. IMO, if you were planning on pushing the turn no matter what hit, I would have just pushed on the flop. I have an AK, TPTK, and depending on the table, that's sometimes a good move.
In this case, I think if you
did push the flop after his raise, he lets the hand go, and you take it down. By waiting to push, you let him catch up.