White plays and wins in 5 moves https://lichess.org/gBN1ZuFl
- Qdd6+ Kh3 2. Qh6+ Kg2 3. Qeh4 Qd1 4. Qh2+ Kf3 5. Q6f4#
The analysis board does checkmate in 5 moves
- Qh4+ Kg2 2. Qd2+ Kg1 3. Qhe1+ Qf1 4. Qg3+ Kh1 5. Qgh2#
Source:
This publication is in my collection "500 chess puzzles. Mate in 5. Advanced & Expert Level."