White plays and wins in 4 moves https://lichess.org/cf7fDduD
- h7+ Kf8 2. h8=Q+ Ke7 3. Qf6+ Ke8 4. Qf7#
The analysis board does checkmate in 5 moves
- h7+ Kg7 2. Rd7+ Kh8 3. Kh6 Rg8 4. hxg8=Q+ Kxg8 5. Rd8#
Source:
This publication is in my collection "500 chess puzzles. Mate in 5. Advanced & Expert Level."