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N-e8+ King moves
N-f7+ King moves
R-g8++
1) N-e8+ K-f8
If 1) .. K-g8 or h8 or h7 2) N-f6+ K-g7 3) R-g8++
2) N-f6+ K-e7 ( 2 .. Kg7 3 R-g8++)
3) R-d7+ K-f8
4) Rxf7++
white Ne8, then Nf6 then Rg8
Ok, how about:
1 Ne8+ Kf8
2 Nxg6+!! (yeah, this variation takes a move longer, but what’s a cool mate without a sacrifice to the chess gods?)
2 …f7xg6
3 Nf6+ Ke7
4 Rd7+ Kf8
5 Rf7++