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