White plays and wins in 4 moves https://lichess.org/8v7v2dVB
- e8=Q+ Qf8 2. Rg4+ Kh8 3. Qh5+ Qh6 4. Qxh6#
The analysis board does checkmate in 5 moves
- e8=Q+ Kh7 2. Qh5+ Kg7 3. Rg4+ Kf6 4. Qg5+ Kf7 5. Qg7#
Source:
This publication is in my collection "500 chess puzzles. Mate in 5. Advanced & Expert Level."