White plays and wins in 3 moves https://lichess.org/6eqw2ci3
- Ng7 Rb2 2. e8=Q+ Kh7 3. Rh4#
The analysis board does checkmate in 5 moves
1.Rg4+ Kh7 2. Rh4+ Kg8 3. Nh6+ Kh7 4. Nf7+ Kg8 5. Rh8#
Source:
This publication is in my collection "500 chess puzzles. Mate in 5. Advanced & Expert Level."