We have two responses for you. One from Penny who can do it with 4 cuts and 5 pieces.

and another from Claude who can get 4 pieces.

The area of the rectangle is 10, so the side of the square should be sqrt(10).

So the question can be rephrased as "Cut a sqrt(10) by sqrt(10) square into 4 pieces, and then put them back into as a 5 by 2 rectangle."

The best way to view the square is to see it inscribed in the 4 by 4 square:

Now all you have to do is cut along the lines to make four pieces that can be made into the 5 by 2 rectangle.

Claude