Below you'll discover the solutions to the "mate in five and more" problems.
I'll give some comments to help you understand the way of thinking that leads to a solution. I hope this helps you to improve.
This forces the Queen or Rook to take the knight. When the Rook takes, the back rank is no longer protected. And when the queen takes, the black queen can enter h3.
3. Qh2, (this leaves the white rook unprotected), Qxf1+;
4. Qg1, Qxg1#;
Taking with the Rook (after move nr.1) leads to:
5. Qg1, Qxg1#
The black king is a little exposed. It's time for a queen sacrifice.