Black plays and wins in 4 moves https://lichess.org/6U7HadcD/black
1... Qh5+ 2. Kg1 Qh6 3. Rc8 Qe3+ 4. Kf1 Qf2#
The analysis board does checkmate in 5 black moves
1... Qa1+ 2. Kh2 Qa2+ 3. Kg1 Qxg8+ 4. Kf1 Qg2+ 5. Ke1 Qe2#
Source:
https://www.amazon.com/Chess-Puzzles-Advanced-Expert-Level/dp/B0917YQZP1