The question is asking to calculate the length of the diagonal $x$ of a rectangle, where the sides are given as 5 and $5\sqrt{2}$.

To find the length of the diagonal in a rectangle, we can use the Pythagorean theorem:

$x = \sqrt{(5)^2 + (5\sqrt{2})^2}$

Let's compute it step by step:

1. Square both sides: $5^2 = 25 \quad \text{and} \quad (5\sqrt{2})^2 = 5^2 \times (\sqrt{2})^2 = 25 \times 2 = 50$

2. Add the squares: $25 + 50 = 75$

3. Take the square root of the sum: $x = \sqrt{75} = \sqrt{25 \times 3} = 5\sqrt{3}$

Therefore, the length of the diagonal $x$ is $5\sqrt{3}$.

Would you like further explanation or details?

Here are some related questions for practice:

1. What is the area of this rectangle?
2. If the diagonal was $10\sqrt{2}$, what would the side lengths be?
3. How do you use the Pythagorean theorem to find the sides of a right triangle?
4. What is the perimeter of this rectangle?
5. If you increase both sides of the rectangle by 2, what will the new diagonal length be?

Tip: The Pythagorean theorem is a useful tool for calculating distances in right-angled triangles, including diagonals in rectangles!