If you think his 5bet is bluffy, meaning he is bluffing more often than he should, just stick it in right there.
Imagine he has J8s or any other 3b-5b bluff hand for that matter. If you jam pre, you are going to win the $300 in the pot right there. If you call his 5bet, there are $370 in the pot on the flop. Do you think you can on average win $300 or more from that pot? That seem's extremely unlikely, even if he is a fishy bad player. It's very difficult to even win back half the pot postflop out of position.. with AQs you might be able to get back more than half, but there is no way that your average return is more than 300/370.
Now that you are on the flop, reads would help. AQcc seems like a hand you should fold, but floating and raising are reasonable. People like to 3b 4b and 5b suited hands, so less likely than normal that either of you has a flush draw, more often you will both have a flush or just no heart. If he has a high cbet I can see both floating and raising working out.
I'm not sure exactly how much I like your minraise. You don't represent much.. but maybe you could have AhTx and play it that way? Maybe AAh? At the same time, if he has nothing, it's difficult for him to float, so I can certainly see this working.
Once he calls flop I think he has a flush somewhat often. Not that he has many flushes to begin with, but hands without a heart fold flop, hands with 1 heart jam flop, so for calling there is kind of only hands with 2 hearts left. So I don't think you can jam turn. River you wouldn't represent anything either so check is good.
