<image>Exploration Question
Figure a is a rectangle with a length of 2m and a width of 2n, which is divided into four smaller rectangles along the dashed lines in the image using scissors, and then assembled into a square as shown in figure b.

(1) What do you think is the side length of the shaded square in figure b? ____
(2) Please find the area of the shaded part in figure b using two different methods.
Method 1: ____
Method 2: ____
(3) Observing figure b, can you write the equal relation between the following three algebraic expressions?
Algebraic expressions: (m+n)^{2}, (m-n)^{2}, mn
(4) Based on the equal relation in question (3), solve the following problem: If a+b=7, ab=5, then (a-b)^{2}=____.