To rationalize the denominator of the given expression $\frac{\sqrt{5}}{\sqrt{3}}$, we eliminate the square root from the denominator by multiplying both the numerator and denominator by $\sqrt{3}$:

$\frac{\sqrt{5}}{\sqrt{3}} \times \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{5} \cdot \sqrt{3}}{\sqrt{3} \cdot \sqrt{3}}.$

Step-by-step solution:

1. Multiply the numerator: $\sqrt{5} \cdot \sqrt{3} = \sqrt{15}$.
2. Multiply the denominator: $\sqrt{3} \cdot \sqrt{3} = 3$.

Thus, the result is:

$\frac{\sqrt{15}}{3}.$

Final Answer:

The simplified expression is:

$\frac{\sqrt{15}}{3}.$

Let me know if you'd like a more detailed explanation!

Related Questions:

1. How do you rationalize a denominator that contains a cube root?
2. What are the steps to rationalize $\frac{\sqrt{2} + 1}{\sqrt{3}}$?
3. How do you handle rationalizing $\frac{\sqrt{5}}{\sqrt[3]{3}}$?
4. What happens when the denominator contains a sum like $2 + \sqrt{3}$?
5. Why is rationalizing the denominator important in mathematics?

Tip: Multiplying by a conjugate is useful when rationalizing denominators with sums or differences involving roots!