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1. Ng3+ Kh4 2. Rg4+ Kh3 3. Rg5+ Rxf5 4. Nxf5 any 5. Rg3#
1.Ng3+ Kh4
2.Rg4+ Kh3
3.Rg5+ Rxf5
4.Nxf5 any move
5.Rg3#
If 3…Kh4, then 4.Rh5#
1. Ng3+ Kh4 2. Rg4+ Kh3 3. Rg5+ Kh4 4. Rh5 mate
I overlooked 3…Rxf5 but after 4. Nxf5 nothing can prevent 5. Rg3 mate!
1. Ng3+ Kh4 2. Rg4+ Kh3 3. Re4+ Rxf5 4. Nxf5 and Rh4# is unavoidable
Unless I am missing somthing really obvious (not for the first time):
1.Ng3+ Kh4
2.Rg4+ Kh3
3.Rf4#
1.Ng3+ Kh4 2.Rg4+ Kh3 3.Rg5+ Rxf5 4.Nxf5 a2 5.Rg3#.