It’s pretty much all been said already, but I’ll still say:
45s in the BB should check preflop, then fold to the first bet, unless you flop a full house or trips, or maybe two pair or an open-ended straight draw.
This flop was a mirage. You hit a pair of 5s, and needed a 3 for a 2-6 straight or two more hearts for a baby flush. I’m guessing that, combined with the check-around at the flop was what made you feel good about the hand.
One possible read at the turn is that no one hit the flop and your 5’s were good. If you were ahead with 5s, a big bet at the flop might have closed the hand down. But that’s a big risk if you get called and all you have is 5s. It’s better to just wait for a better hand to risk your chips on.
If I was in your situation and going to try to take the hand, I’d treat it like a steal situation and make the bet pot-sized or overbet the pot, maybe even shove. If you’re right and no one has anything, you’ll take the hand, but when you do that you’re risking your entire stack for what’s in the middle. Whether it’s worth it or not depends entirely on how likely your opponents still in the hand are likely to call you.
You have to ask yourself how many times can you get the table to fold before one call busting you makes it no longer worth it, and then sense how likely the people at the table are to fold that many times. Because odds are, a pair of 5s with a inside draw to a low straight is going to get beat when it gets called.
I can understand why you tried to bet on the Turn though. The action on this hand is very slow, making it tempting to try to take the pot. You could have maybe done that, with a bigger bet, although given what shanefoolr held that wasn’t going to happen at the turn. Once he raised, you should have realized you were beat and let it go. Shoving when you did, it was too little too late. It wasn’t likely to induce him to fold, and so you should have only done it if you were certain you would prevail in the showdown. A pair of 5s doesn’t assure this type of certainty.
Still, it could have went the other way if you had rivered a heart. But then, playing low flushes is a bad bet in the long run anyway.
I will say it’s better that you lose this hand and learn the right lessons from it than to win it and think it was a good play and let that inform your future play. So, good experience here.