White plays and wins in 4 moves https://lichess.org/tIgO40iy
- Ke3 Kg5 2. Qf7 Kg4 3. Qg6+ Kh3 4. Qg3#
The analysis board does checkmate in 5 moves
- Ke3 Kf6 2. Kf4 Kg7 3. Kf5 Kh7 4. Kf6 Kh6 5. Qg6#
Source:
This publication is in my collection "500 chess puzzles. Mate in 5. Advanced & Expert Level."