Black plays and wins in 2 moves https://lichess.org/Sd0vEqEr/black
1... h2+ 2. Kf1 h1=Q#
The analysis board does checkmate in 5 moves
1... h2+ 2. Kg2 Re2+ 3. Kh1 Kh3 4. Rg1 hxg1=Q+ 5. Kxg1 Re1#
Source:
This publication is in my collection "500 chess puzzles. Mate in 5. Advanced & Expert Level."
