First of all, I'm a little confused how you can read him for a draw simply based on him calling your bets.  I think most players would call with a weak J, any T, any 5, because you have air a good amount of the time and they don't want to turn their hand into a bluff.

Anyway, lets assume he does have draw.  If he has hearts or QK, you are ahead on the river but he will clearly fold to a bet.  If he has 9Q you are crushed and he is never folding.  If he has 89 you are behind and he might fold.  By betting you lose money to 9Q and maybe gain money from 89, but who knows?  It seems like a marginal river bet at best.

Going further and assuming he may have had the best hand on the flop, what do you think he does?  If I am in villains spot I would probably fold my 5s to your 3rd barrel, but he is obviously never folding a T and I don't think he's folding a J either.

I think your hand is good some percentage of the time, but you shouldn't be happy check/calling because he has a decent number of pairs and a few straight here.  I make a defensive bet of maybe 30,000 here and fold to a raise.

In general, I think your post shows a misunderstanding of HU play.  Why are you trying to rep a boat or an overpair?  Those hands are so infrequent HU compared to the times when one pair is the winner.