Here's how I would play it according to your description of the player:

Flop: I would throw in a probe bet here (3-4 dollars) trying to induce him to come over the top. If he does I push and hope he doesn't have pocket fives.

Turn: If he just calls the flop I would check the turn. Maybe his hand improved or maybe he thinks you may have backed down because your c-bet was called.

River: Shove.