blacks best move

?  What am I missing... K to either dark square closer to white king, check, white must either block with Q or move king into mated position, and blocking just extends it one move?

Black also has forced mate (in 5) via 1...Qa1+ (1...Qh8+ doesn't have the same effect because once the King moves to g1, d4 is unavailable for the Black Queen) 2.Kh2 (2.Qf1 Qxf1+ is mate next move; 2.Qc1 Qxc1+ 3.Kh2 Qd2+ 4.Kh3 Qg2+ 5.Kh4 Qg4#) 2...Qe5+ 3.Kh1 (3.Kh3 Qg3#; 3.Kg1 Qg3+ with mate the following move; 3.Qf4+ Qxf4+ 4.Kh1 Qg4 5.Kh2 Qg2#) 3...Qe1+ 4.Kh2 Qg3+ 5.Kh1 Qg2#

The discovery is faster, but if you were looking for a way to execute without involving discoveries.