Black plays and wins in 5 moves https://lichess.org/nTBCVbhF/black
1... Rg2+ 2. Kh1 Rxg3 3. Rb1 f2 4. Rf1 Rg2 5. Ra1 Rh2#
The analysis board does checkmate in 5 moves
1... Rg2+ 2. Kh1 f2 3. Rxf2 Rxf2 4. Kg1 Kxg3 5. Kh1 Rf1#
Source:
This publication is in my collection "500 chess puzzles. Mate in 5. Advanced & Expert Level."