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1 Qe8
2 h4
3 Ne3 ..Kh3, Qe6,
…Kf3, Qh5
then Mate
1. Qe8+ Kg5
2. h4+ Kg4
3. Ne3+ Kf3
4. Qh5+ Kxe4
5. Qf5#
1. Qe8+ Kg5 2. h4+ Kg4 3. f3+ Kxf3 4. Qh5+ Kxe4 Qg4# also works.
But, 3. Ne3+ is better because of 3. … Kh3 4. Qe6+ f5 5. Qxf5# which isn’t available if the N stays on f5