Black plays and wins in 3 moves https://lichess.org/F2jzm5JJ/black
1... h3+ 2. Kg1 Qf3 3. Bf4 Qg2#
The analysis board does checkmate in 5 moves
1... h3+ 2. Kg1 Qb6+ 3. Kh1 Qb7+ 4. Rf3 Qxf3+ 5. Kg1 Qg2#
Source:
This publication is in my collection "500 chess puzzles. Mate in 5. Advanced & Expert Level."
