[glen]

hand 1: If someone doesn't think you would play a 5 that fast, they will very likely cap the flop KJ or AJ. You need to check-raise the turn here, and the thinking when the 6 hit, "The river was a 6. Hmmmm...56suited would surely be a limping hand in this game. I checked and called." yuck. Check-raise anyways and call a 3 bet. The river check-raise should seem odd in the context of the hand for obvious reasons anyways so that you will get paid off by worse hands . . .

Hand 2: Bet the turn. Like you said, you have the second nut draw, and the flop was check-call. . .