My only question here is, if it is ok to bet 1/3 pot after villain checks OTF?
PokerStars - $0.02 NL (6 max) - Holdem - 6 players
Hand converted by PokerTracker 4
BTN: 101 BB
SB: 110 BB
BB: 162 BB
UTG: 101 BB
Hero (MP): 101 BB
CO: 141 BB
SB posts SB 0.5 BB, BB posts BB 1 BB
Pre Flop: (pot: 1.5 BB) Hero has A♠ 5♠
fold, Hero raises to 3 BB, fold, fold, fold, BB raises to 9.5 BB, Hero calls 6.5 BB
Flop: (19.5 BB, 2 players) A♦ 7♣ 3♠
BB checks, Hero bets 6.5 BB, BB raises to 38.5 BB, fold,
I would personally check behind for pot control. We have some potential to improve and want to see more cards, while we absolutely do not want to get check / raised on the flop. Our hand as it stands has about 1 - 1.5 streets of value and there is no need to start betting on that dry board. Any 2, 4, 5 ,6 and spade would give us much more equity and options.
1/3 seems asking for trouble. In a way it accomplishes nothing because you give him the change to value check-raise or even bluff-check-raise or call with the right pot odds for almost anything.
Of course we hit, but we can't play for stacks with a 5 kicker. If Turn is a more favorable hand for a FD,SD etc then yes we could be more aggressive.
and always always always what info you have for villain so far?
as a general guideline, i don't stab wide boards that hit the villain's range, such as high card boards. flop is an easy check, and we should probably still get away if villain starts to bet big.
Ok call pre, flop I check back: you don't bet atc, you need some top pair with check back, you havent'3 street and if oppo want bluff board Axx is perfect, he has almost always showdown value.
Pot control is the way 
As played vs big raise ok bet fold
" Stay Humble, Stay Hungry " 
