Black plays and wins in 3 moves https://lichess.org/G7YFskrT/black
1... Kg3 2. Rb2 Nh3+ 3. Kh1 Rxf1#
The analysis board does checkmate in 5 moves
1... Kg3 2. Rf2 Nh3+ 3. Kh1 Nxf2+ 4. Kg1 Nh3+ 5. Kh1 Rxf1#
Protecting the bishop, blacks lasted longer.
Source:
This publication is in my collection "500 chess puzzles. Mate in 5. Advanced & Expert Level."