To simplify \( \frac{5}{3\sqrt{5}} \) and rationalize the denominator, we can multiply the numerator and the denominator by \( \sqrt{5} \):
\[ \frac{5}{3\sqrt{5}} \cdot \frac{\sqrt{5}}{\sqrt{5}} = \frac{5\sqrt{5}}{3 \cdot 5} \]
Calculating the denominator:
\[ 3 \cdot 5 = 15 \]
Thus, we have:
\[ \frac{5\sqrt{5}}{15} \]
Now, we can simplify the fraction:
\[ \frac{5\sqrt{5}}{15} = \frac{\sqrt{5}}{3} \]
Therefore, the exact answer is:
\[ \frac{\sqrt{5}}{3} \]