I think you can either check/fold or bet/fold (and probably give up on the river). The flop hits a limper's range pretty hard and the 9 isn't a good card, so I'd lean towards check/folding. I guess if you had a strong read that he was very loose preflop and peels very lightly on the flop but gives up on the turn, then a bet/fold line makes more sense.
QJ got there, J9 and Q9 made a pair + gutshot, and you're behind to other aces he might limp and keep calling with like AJ or AQ. So you're probably only beating fives and maybe some weaker aces he didn't feel like folding on the flop. He could have a pocket pair but that's less likely, both because they are less common anyway and also because he might fold those on the flop. I'd probably just check and hope he lets you show it down for free.
I bet this turn and then check/folded the river. I thought the turn bet was useless. As weak as it seems I should have just folded this here I think. Unless I have some read or some information that he's just firing air on the turn, I think it's better to fold since all of the cards by the turn are right in the middle of his range.