Black plays and wins in 3 moves https://lichess.org/J7QbwoBl/black
1... f2+ 2. Rxf2 Rxf2 3. Kh1 Rf1#
The analysis board does checkmate in 5 moves
1... Rg2+ 2. Kh1 f2 3. Rxf2 Kxf2 4. g7 Rxg7 5. Kh2 Rh7#
Source:
This publication is in my collection "500 chess puzzles. Mate in 5. Advanced & Expert Level."