Well, he could just be a bad player calling with 4H 5H. Especially if he makes a lot of loose calls. However, if you take into account he has position with the button, it's not the worst call with a suited connector. People tend to call a lot more off the button. If he put you on two big cards and he hit a pair, with like a 7 high flop, he thinks he's probably good.

Personally, I probably wouldn't make the call unless I had a couple of other callers coming in boosting the pot odds. However, you do have to mix your play a bit so your not too predictable.

I saw the range of hands you put this guy in and, in general, that is a good range to put someone one, but not when they are on the button. You have to open up to the possibilities of more hands in that case.

$3.50 on turn.
As played, Check fold river. He doesn't turn his 5x into a bluff nearly ever.
$6.50 into a pot of $15, so you're getting 2.3-1 which seems decent odds but it's effectively readless. Just fold and save yourself the hassle. He needs to bluff with all of his missed hearts for you to call profitably here.

I like button. Yeah, I'm doubting that I'm calling that river bet with a 4 card straight/trips/fh out there. I mean I don't think you're good enough times to justify.

bet twice as big on the turn and shove the river

Bet way bigger on the turn. As played, probably just fold. In theory he has a lot of heart combos he should be bluffing with, but in practice no one ever has the stones to shove in their stack on a bluff.

I rarely think he will bluff river when you check so if you are going to call his river shove you should just shove the river. He will pay you off with worse hands that would check behind.