Why is it not a mate?

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AftabAdeel

I was learning through a masterclass of Garry Kasparov and this is a screenshot of the game. Garry, instead of moving the queen to h1, moved the pawn to h5. While, I think Queen to h1 is a mate, why is it not a mate? Garry is playing as black

CombativeRailway

I'm no expert but it looks like if black moves queen to h1 instead of pawn to h5, white king can still escape to g4.

Falconer999

Moving the pawn to H5 set up a potential mate on the next move if black moves Qh1.  Like Combative Railway said, if the queen had moved to h1 first, then the K could move to g4.  Now with the pawn at h5, it cannot move there.