
Solution

1. Qe7+ Kg8 2. Rxg6+, followed by Qxc5
Or
1. Qe7+ Kh8 2. Qxf8+
Or
1. Qe7+ Bf7 (or Rf7) 2. Rxg6+ still gets the black queen, Qxc5.
1. Qe7+ Kg8 2. Rxg6+, followed by Qxc5
Or
1. Qe7+ Kh8 2. Qxf8+
Or
1. Qe7+ Bf7 (or Rf7) 2. Rxg6+ still gets the black queen, Qxc5.