From the "Chess Akt" book "500 chess puzzles".
Subtitle: Mate in 5. Advanced & Expert Level.
Black plays and win in only 3. See the winning moves at https://lichess.org/JKiQn5qN
1... Kc6 2. a7 Rh2 3. Kb8 Rh8#
The title of the book should be "Mate in 5 or less" ;)
Anyhow, placing the pieces again in the analytics board, the computer calculated the checkmate after 5 moves, keeping the pawn in place.
1... Kc6 2. Ka7 Rf2 3. Kb8 Rf7 4. Ka8 Kb6 5. a7 Rf8#
Following a similar strategy, but moving the king next to the pawn to force its advance, the checkmate is performed in 4 moves only.
1... Kc6 2. Ka7 Rh2 3. Ka8 Kb6 4. Kb8 Rh8#