White plays and wins in 4 moves https://lichess.org/rKJVdJPu
- g8=Q+ Kxh6 2. Qe6+ Kh7 3. Rd7+ Kh8 4. Qe8#
The analysis board does checkmate in 5 moves
- g8=Q+ Kxh6 2. Qe6+ Kh5 3. Rh8+ Kg5 4. Rg8+ Kh5 5. Qh3#
Source:
This publication is in my collection "500 chess puzzles. Mate in 5. Advanced & Expert Level."