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1.Rxh5+ Kxh5 ( 1. …Kg6?? 2.Qf7# or 1. …Kg7?? 2.Qf7# ) 2.Qf7+
(a) 2. …Kg4 3.Qf3+ Kh4 4.Rh1+ Qh3 5.Qxh3# or Rxh3#
(b) 2. …Kh4 3.Rh1+ Qh3 ( or 3. …Kg4 4.Qf3# ) 4.Rxh3+ Kg4 5.Qf3#
(c) 2. …Kh6 3.Rh1+ Qh3 4.Rxh3#
Well done!