I think you made a good call with that extra 9 on the river Biscuit.
If that 5 of spades were perhaps a J of spades, then raise the pot.
Many of us have called with a river card like that and beaten by a full house or your opponent has the AX of spades as well, or the nut flush as propiper mentioned. I have seen this several times thinking my K-high flush would take it.
But since you mentioned that your K-high flush had great action, I am thinking you won this pot.