White plays and wins in 5 moves https://lichess.org/XqX3H8bq
- Qb1 Rh2 2. Kc3 Rh1 3. Qxh1 Ka2 4. Kc4 Ka3 5. Qa1#
The analysis board also does checkmate in 5 white moves
Qc3+ Ka4 2. Kc4 Rc2 3. Qxc2+ Ka5 4. Qg6 Ka4 5. Qa6#
Source:
https://www.amazon.com/Chess-Puzzles-Advanced-Expert-Level/dp/B0917YQZP1