Mate in 5 Exercise 39

White plays and wins in 3 moves https://lichess.org/sVWYD8aE

1. Qxg3+ Kh1 2. Qh3+ Rh2 3. Qf1#

The analysis board does checkmate in 5 moves

1... Kh1 2. Kh3 Re2 3. Qf3+ Kg1 4. Qxe2 Kh1 5. Qe1#

Source:

This publication is in my collection "500 chess puzzles. Mate in 5. Advanced & Expert Level."