Black plays and wins in 3 moves https://lichess.org/rgoYLMYG/black
1... Qf4+ 2. Rg3 Qxg3+ 3. Kh1 Qg2#
The analysis board does checkmate in 5 moves
1... Qg2+ 2. Rxg2+ hxg2 3. Kh3 g1=Q 4. Kh4 Qg6 5. Kh3 Qg3#
Source:
https://www.amazon.com/Chess-Puzzles-Advanced-Expert-Level/dp/B0917YQZP1