To simplify \(\frac{\sqrt{95}}{3\sqrt{5}}\), we start by simplifying the square roots.
We can rewrite \(\sqrt{95}\) in terms of \(\sqrt{5}\):
\[ \sqrt{95} = \sqrt{19 \cdot 5} = \sqrt{19} \cdot \sqrt{5} \]
Now, substituting this back into the original expression gives:
\[ \frac{\sqrt{95}}{3\sqrt{5}} = \frac{\sqrt{19} \cdot \sqrt{5}}{3\sqrt{5}} \]
Since \(\sqrt{5}\) in the numerator and the denominator can be canceled out (as long as \(\sqrt{5} \neq 0\)), we have:
\[ \frac{\sqrt{19} \cdot \sqrt{5}}{3\sqrt{5}} = \frac{\sqrt{19}}{3} \]
Thus, the exact answer is:
\[ \frac{\sqrt{19}}{3} \]