Its a must that the Hero pushes all in here - a relative no brainer here.
The problem is the hand was played wrong from the flop IMO..
Assuming that both players are top notch players, and that both play a somewhat tight/aggressive game like most pros...this is how the pot IMO should have gone.
pre-flop action...exactly what you want. 1 opponent against a big pp. Good.
Flop gives you top set, with a possible flush and straight draws. Hero should strongly consider a check-raise to steal the pot outright here. There are too many draws IMO to WANT to play this to the end. Yes, you flopped the nuts, but its quite possible that you are an underdog to the hand if he has TJh. (of course we know he doesn't have hte 10h because it comes on the river, but as of this moment hero does not know this). TJh is a very possible hand, the best suited connector aside from AK imo, since every straight flopped is the nuts. ANYHOW - if he bets off of your check, which he should when you check, he should put you on a medium pair like 99, you raise him all in right then - this is Opprotunity 1 to win the pot even if the cards to come would give it to him.
Lets pretend that he didn't check. IMO 5k is too low. Sure, its over-sized, but i'd make a 2x the pot bet at this if i didn't check. He's now gettnig HORRIBLE odds to continue his draw (if he's drawing at one hand, not one of two
hands). an 8k bet here is better IMO than a 5k bet. It still leaves you with 10k in chips. He calls. Turn comes 9. If he was playing TJh he just made his straight. You've shown aggression - no use stopping. Here is where you should make your decision to check or to push. Pushing IMO is the right call. If he calls, you're either beaten, or he was on the flush draw. To JUST be on a gutshot to call for 10k is a lousy call, and if he makes his draw, you just have to grin and bear it. Even 18k to chase a flush to the river is borderline psycotic IMO. By pushing on the turn you get your second opprotunity to win the pot right out. If he folds two hearts or a jack, the 10 doesn't come and hero wins the pot. If he calls with 2 hearts or a jack, you STILL went in with the best hand, and he sucked out. Sometimes you gotta pay a man off.
If you are still betting when the river card comes as the above situation states, then you're almost 100% beaten, but you're pot comitted anyways. You might as well fire the last 5k into the pot and hope against the odds he didn't have a flush or straight draws and had a big pocket pair like AA or QQ, or even a small one like 88 and didn't play it correctly. But all evidence points to a draw since he didn't raise your bets with an overpair (AA) or a set on the flop (88 or QQ). Any number of hands beat you any 2 hearts, 67, any or any J. I'd say you squandered your opprotunity to get a relatively large pot.