Black plays and wins in 2 moves https://lichess.org/SweniHx6/black
1... f4 2. Qc1 Qg2#
The analysis board does checkmate in 5 moves
1... f4 2. Qc3+ Qe3 3. Qxe3+ fxe3 4. Kg1 e2 5. Kh1 e1=Q#
I would rather block with the pawn instead of exchanging queens.
Source:
This publication is in my collection "500 chess puzzles. Mate in 5. Advanced & Expert Level."
