The expression in the image is:

$\frac{5}{\sqrt{10} + \sqrt{5}}$

To simplify this, we can rationalize the denominator by multiplying both the numerator and the denominator by the conjugate of the denominator. The conjugate of $\sqrt{10} + \sqrt{5}$ is $\sqrt{10} - \sqrt{5}$.

Let's go step by step:

1. Multiply the numerator and the denominator by $\sqrt{10} - \sqrt{5}$:

$\frac{5}{\sqrt{10} + \sqrt{5}} \times \frac{\sqrt{10} - \sqrt{5}}{\sqrt{10} - \sqrt{5}} = \frac{5(\sqrt{10} - \sqrt{5})}{(\sqrt{10} + \sqrt{5})(\sqrt{10} - \sqrt{5})}$

2. Simplify the denominator using the difference of squares formula:

$(\sqrt{10})^2 - (\sqrt{5})^2 = 10 - 5 = 5$

So, the expression becomes:

$\frac{5(\sqrt{10} - \sqrt{5})}{5}$

3. The $5$s cancel out, and we are left with:

$\sqrt{10} - \sqrt{5}$

Thus, the simplified expression is:

$\sqrt{10} - \sqrt{5}$

Would you like further clarification on any part? Here are some related questions for practice:

1. How do you rationalize a denominator involving a sum of square roots?
2. What is the difference between a sum and difference of squares in terms of simplification?
3. Can you simplify $\frac{7}{\sqrt{3} + \sqrt{2}}$ using the same method?
4. What are conjugates and why are they useful in rationalizing denominators?
5. What happens if you have a complex number in the denominator? How do you rationalize it?

Tip: Rationalizing the denominator helps avoid square roots or irrational numbers in the denominator, making expressions easier to work with.