White plays and wins in 3 moves https://lichess.org/NTfG0cPS
- Qb4+ Kf5 2. Qe6+ Kg5 3. Qbg4#
The analysis board does checkmate in 5 moves
- Qb4+ Rc4 2. Qbxc4+ Kf3 3. Qc3+ Kf2 4. Qgg3+ Kf1 5. Qce1#
The same start but sacrificing the tower to last a little longer
Source:
This publication is in my collection "500 chess puzzles. Mate in 5. Advanced & Expert Level."