Black plays and wins in 3 moves https://lichess.org/vjz0hXW6/black
1... Rg2+ 2. Kh1 Bf2 3. Rc1 Rh2#
The analysis board does checkmate in 5 moves
1... Rg2+ 2. Kh1 Bf2 3. Rxf2 Rxf2 4. Kg1 Rf8 5. Kh1 Rf1#
Source:
This publication is in my collection "500 chess puzzles. Mate in 5. Advanced & Expert Level."