
White to move and mate in 5.
Answer:
1. Qe3; Pg5
2. Rg1; Pg6 or Pg4
3. Qc5; Pg6, Pg5, or Pg3
4. Qxa3 and Black can’t prevent either 5. Qxb2 mate or, if 4. …Qxc3, 5. Qxc3 mate

White to move and mate in 5.
Answer:
1. Qe3; Pg5
2. Rg1; Pg6 or Pg4
3. Qc5; Pg6, Pg5, or Pg3
4. Qxa3 and Black can’t prevent either 5. Qxb2 mate or, if 4. …Qxc3, 5. Qxc3 mate