Bring it

No one has any idea you have a hand here, and I'm not willing to give that information up so readily on 4th. If you had aces up at that point it would be different. If you do just call, and go on from 4th and make an open pair, many people will assume your other pair is 3's, and misplay the hand badly. Yes, getting an extra bet in on 4th with aces makes you a little extra in the hand, but I think you would do better in the long run by letting the hand develop. You may even get a check-raise or raise opportunity on 5th or 6th by waiting.

In my opinion, the river 5 doesn't change your hand much, unless someone has a set. In that case I think you'd have heard from them by now, or they back into a set on the river, again unlikely. Given the straight and flush possibilities out there, I'm inclined to check and call. If it is bet and raised back to me, unless you know both players are likely to go nuts on the river for some reason, it is an easy fold.

Checking also lets K's up bet if they want, and you can see if the third hand raises. If someone wants to argue for a bet on the river, I can see the point, but I don't think I'm getting called by one pair, and the odds seem higher that a draw in either hand gets there rather than just 2 pair.