To solve the expression $\frac{10}{\sqrt{5} + \sqrt{2}}$, we should first rationalize the denominator. This involves multiplying both the numerator and the denominator by the conjugate of the denominator.

Step 1: Identify the conjugate

The conjugate of $\sqrt{5} + \sqrt{2}$ is $\sqrt{5} - \sqrt{2}$.

Step 2: Multiply the numerator and denominator by the conjugate

$\frac{10}{\sqrt{5} + \sqrt{2}} \times \frac{\sqrt{5} - \sqrt{2}}{\sqrt{5} - \sqrt{2}} = \frac{10(\sqrt{5} - \sqrt{2})}{(\sqrt{5} + \sqrt{2})(\sqrt{5} - \sqrt{2})}$

Step 3: Simplify the denominator

Using the difference of squares formula, $(a + b)(a - b) = a^2 - b^2$, we get: $(\sqrt{5})^2 - (\sqrt{2})^2 = 5 - 2 = 3$

Step 4: Simplify the expression

Now the expression becomes: $\frac{10(\sqrt{5} - \sqrt{2})}{3} = \frac{10\sqrt{5} - 10\sqrt{2}}{3} = \frac{10\sqrt{5}}{3} - \frac{10\sqrt{2}}{3}$

So, the simplified form of the expression is: $\frac{10\sqrt{5}}{3} - \frac{10\sqrt{2}}{3}$

Would you like any further details or explanations?

Here are some related questions you might find helpful:

1. How do you rationalize the denominator of a fraction?
2. What is the difference of squares formula, and how is it applied?
3. How do you simplify expressions involving square roots?
4. What is the conjugate of a binomial expression, and why is it useful?
5. How can you simplify complex fractions?

Tip: When rationalizing the denominator, always multiply by the conjugate to remove the square roots from the denominator.