I recently moved up to NL5 and one thing that I notice is that regulars c/r my range c-bets way more often than it was the case on NL2. I feel secure about my calling range on the flop on boards that allow me to range c-bet in the first place. However, I'm often unsure how to proceed on turns and rivers.

In this particular hand, I range c-bet on 932r (as on all MLLr boards when playing vs. BB) and get c/r. Ace high with BDFD goes into my calling range. Villain checks turn (as he should with most of his holdings). What am I supposed to do on turn and river here? Both with this particular holding and more in general...

Turn: I picked up quite some equity. Is this a bet? In game I thought it might be even too strong for betting and I might just go for full equity realization with a checkback, whereas flush draws with lower overcards (Kx, Qx) could go into my betting range.

River: Villain's two checks just let's me think that his range his probably pretty showdown-heavy. Against the blank, I don't give myself much fold equity vs. these types of hands and A5 (though an unlikely holding) has improved to a straight now.