The problem asks for an expression representing the area of the shaded region. Here's how we can solve this:

1. Area of the large square: The large square has a side length of $x$. The area $A_{\text{square}}$ of this square is: $A_{\text{square}} = x^2$

2. Area of the smaller rectangle: The small rectangle has dimensions 5 (height) and 2 (width). The area $A_{\text{rectangle}}$ of the rectangle is: $A_{\text{rectangle}} = 5 \times 2 = 10$

3. Area of the shaded region: The shaded region is the area of the large square minus the area of the small rectangle: $A_{\text{shaded}} = A_{\text{square}} - A_{\text{rectangle}} = x^2 - 10$

Thus, the expression representing the area of the shaded region is: $\boxed{x^2 - 10}$

Would you like more details or have any questions? Here are some related questions to expand the topic:

1. How would the expression change if the dimensions of the small rectangle were different?
2. What is the area of the shaded region if $x = 6$?
3. How would you express the perimeter of the large square in terms of $x$?
4. What would happen to the shaded area if the rectangle's width doubled?
5. How can this problem be generalized to any square with a smaller rectangle subtracted from it?

Tip: Always subtract the areas of removed parts when calculating the area of complex shapes.