Black plays and wins in 3 moves https://lichess.org/P9DLYIqg/black
1... Kg3 2. Rc3 Rb1+ 3. Rc1 Rxc1#
The analysis board does checkmate in 5 moves
1... Kg3 2. Ra1 Rh2+ 3. Kg1 f3 4. Rf1 Nxf1 5. Kxf1 Rh1#
It was a better choice for the white tower to guard row 1.
Source:
This publication is in my collection "500 chess puzzles. Mate in 5. Advanced & Expert Level."