Black plays and wins in 4 moves https://lichess.org/DvtwhFBZ/black
1... Qe2+ 2. Kg1 Kh3 3. Qc8+ Kg3 4. Qc1 Qg2#
The analysis board does a similar checkmate in 5 moves
1... Qd2+ 2. Kg1 Kg3 3. Qc3+ Qxc3 4. Kf1 Qd2 5. Kg1 Qg2#
Source:
This publication is in my collection "500 chess puzzles. Mate in 5. Advanced & Expert Level."
