Party Poker 2/4 Hold'em (8 handed) converter

Preflop: econ_tim is SB with K:spade:, Q:spade:.
5 folds, Button calls.

Flop: (7 SB) A:spade:, 5:spade:, 5:heart: (2 players)
econ_tim bets, econ_tim calls.

Turn: (5.50 BB) 9:heart: (2 players)
econ_tim checks, Button bets, econ_tim calls.

River: (7.50 BB) 7:diamond: (2 players)
econ_tim checks, ...

Preflop I'm comfortable with.

Flop I don't know if bet/call, check/raise, or bet/3-bet is best.

And if I bet/call the flop, should I gaybet the turn?

Villain is unknown, although I suspect he is more aggressive and slightly better than average player.

I would have played it the same way. It's very reasonable for the button to have any A (or even a random 5) and after getting raised on the flop and him NOT taking a free card I check/fold the river.

Zara

Tim, I would strongly consider 3-betting this flop, or donking the turn.

I find a lot of opponents lately are raising the HU flops with air. The pair on the board makes it unlikely that your opponent connected with it. He could be raising here with a mid pp, or absolutely nothing, and he's testing the waters with a raise.

Of course, this play is read dependent. If the button does not usually try to steal, or is passive, you should probably just play as if you were trying to hit your draw.