Black plays and wins in 3 moves https://lichess.org/UzrZEEuF/black
1... Qd2 2. Rg3 Kf1+ 3. Rg2 Qxg2#
The analysis board does checkmate in 5 moves
1... Qg2+ 2. Rxg2+ hxg2 3. Kh3 g1=Q 4. Kh4 Qg6 5.Kh3 Qh5#
Source:
This publication is in my collection "500 chess puzzles. Mate in 5. Advanced & Expert Level."