Black plays and wins in 3 moves https://lichess.org/DgPV2kEE/black
1... Qf4+ 2. Rg3 Qxg3+ 3. Kh1 Qg2#
The analysis board does checkmate in 5 moves
1... Qe4 2. Rf1+ Kxf1 3. Kg3 h2 4. Kh3 Qg2+ 5. Kh4 h1=Q#
Source:
https://www.amazon.com/Chess-Puzzles-Advanced-Expert-Level/dp/B0917YQZP1