I consider myself lucky to have survived this hand. Afterwards, I wondered how I even got involved. Button had been playing any 2 cards to see the flop. I think my play on the turn was where I went wrong, but I'm interested in your analysis.

PokerStars No-Limit Hold'em Tourney, Big Blind is t600 (4 handed) converter

SB (t12240)
Hero (t14513)
UTG (t12038)
Button (t28709)

Preflop: Hero is BB with , .
UTG calls t600, Button calls t600, SB completes, Hero checks.

Flop: (t2250) , , (4 players)
SB checks, Hero checks, UTG bets t600, Button calls t600, SB folds, Hero calls t600.

Turn: (t4050) (3 players)
Hero checks, UTG checks, Button bets t1800, Hero calls t1800, UTG folds.

River: (t7650) (2 players)
Hero bets t1000, Button calls t1000.

Final Pot: t9650

Results in white below:
Hero has 5d Ac (straight, five high).
Button has 7h 9h (flush, nine high).
Outcome: Button wins t9650.