Mate in 5 Exercise 40

White plays and wins in 4 moves https://lichess.org/tIgO40iy

1. Ke3 Kg5 2. Qf7 Kg4 3. Qg6+ Kh3 4. Qg3#

The analysis board does checkmate in 5 moves

1. 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."