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1. Ne8+ Kg5 ( 1. … Ke6 2. Qxe7# )
2. f4+ Kxf4
3. Qh4+ Ke3
4. Qf2+ Ke4
5. Qf3#
James has found the main line. I can only add that a variant arises with 4) Qg3+, and if instead Ke2, 5) Qf2#
The Black pawn on a2 is a fairly reliable indication that the solution has to be something on the lines of “check, check, check, …. and mate”.
1. Ne8+ Kg5 (1. … Ke6 2. Qxe7 mate)
2. f4+! Kxf4
3. Qh4+ Ke3
4. Qd4+ Ke2
5. Qd2 mate