To find the sum of \( 3\sqrt{5} \) and \( 5\sqrt{9} \), we start by simplifying \( 5\sqrt{9} \).
Since \( \sqrt{9} = 3 \), we have:
\[ 5\sqrt{9} = 5 \times 3 = 15 \]
Now, we will add \( 3\sqrt{5} \) to \( 15 \):
\[ 3\sqrt{5} + 15 \]
This expression consists of a radical term \( 3\sqrt{5} \) and a rational term \( 15 \).
Next, we check if the entire sum \( 3\sqrt{5} + 15 \) can be simplified further. Since \( 3\sqrt{5} \) is not a rational number (because \( \sqrt{5} \) is irrational), the whole expression \( 3\sqrt{5} + 15 \) remains irrational, as the sum of a rational number and an irrational number is always irrational.
Thus, the final answer is:
\[ 3\sqrt{5} + 15 \]
Conclusion: The result is irrational, and it is in simplest form.