$10 NLHE 6-max: What will you do if you are in my position?

In the big blind I got K5s all folds to small blind, he raised 3bb so I called.

Flop: 5h5sAc

he raised third of the pod, I called
Turn: J of hart

he raised to 0.70$, I Reraised to 2.45$, he calls
River A of Spades

he checks, I put him of Ace and Checked, He had 67 of heart so he had a flush draw in the turn, I you were me what would you do raise or check it down?

K5 clubs

55AJA

Definite check. You already have a built pot and you're super lucky they didn't have an ace or two in their hand.

I would have played the hand the same way you did and check the river.

I like your flop flat call and river raise. You are getting value out of his draw hands for sure.
Ax is a definite holding. Unless you have bet sizing tells, you played this very well.

What about a raise on the flop though? You will fold out his bluffs, but you will get called by a lot of his aces. You can size a bet on the turn... in this spot you might make a bit more money against his range that way.

A9+, worse 5s (45s, 56s, maybe 57s) will call- this is a good chunk of his c bet flop range.