Black plays and wins in 3 moves https://lichess.org/xGAFmzAs/black
1... h2+ 2. Kh1 Kh3 3. Ra1 g2#
The analysis board does checkmate in 5 moves
1... h2+ 2. Kg2 Rb2+ 3. Kh1 Kh3 4. Rg1 hxg1=Q+ 5. Kxg1 Rb1#
Source:
This publication is in my collection "500 chess puzzles. Mate in 5. Advanced & Expert Level."