Only... 6 I think?
Usually these are a lot more annoying to count, but this one seems straightforward.
I count 7 ;)
Rc5 isn't mate though.
I counted 6
6
I am assuming we are only allowed to checkmate in one move.
Qf8, Qg8, Qe8, Qd7, Qd6, Qc7
It looks like Qf5 works, but black can take the queen with the pawn.