White plays and wins in 4 moves https://lichess.org/CSLnPEa6
- Re8 Rh8 2. Rxh8+ Kxh8 3. f8=Q+ Kh7 4. Qg7#
The analysis board does checkmate in 5 moves
- Re7 Rg8+ 2. fxg8=Q+ Kxg8 3. Rc7 Kh8 4. Kg6 Kg8 5. Rc8#
I didn't play this safe. If the tower captured my pawn, I'd be in trouble.
Source:
This publication is in my collection "500 chess puzzles. Mate in 5. Advanced & Expert Level."