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White mops up after 1. Re8+ Q:e8 2. feQ+ K:e8, with a choice of 3. Qe4+ and 4. Q:h1 or 3. Q:a4+ I like the latter, because the R1 is still exposed and the Q-side pawns are deprived of a defender along the way. For example, the black K must move off the e-file to avoid Qe4+ picking up the R immediately. 3…Kd8 4. Qc6 generates a lot of mating threats quickly. 3…Kf8 4. Nc7 threatens mate via Qe8. 3…Kf7 4. Qd7+ will quickly allow white to get the Q to e4 with check.
1. Re8+ Qxe8
2. fxe8=Q+ Kxe8
3. Bg6+
If 3. … Kd7
4. Qf7+ Kc8 or Kd8
5. Qc7#
If 3. … Ke7
4. Qf7+ Kd8
5. Qc7#
If 3. … Kd8
4. Qxd6+ Kc8
5. Qc7#
Like Anup, I see mate in 5 total moves in all the lines after 3.Bg6+. The king just can’t avoid being pushed into d8/c8.