Suppose that a polynomial function of degree 5 with rational coefficients has the given numbers as zeros. Find the other zero(s).
\[
-\frac{1}{3}, \sqrt{5},-3 i
\]
The other zero(s) islare
(Type an exact answer, using radicals and $i$ as needed. Use a comma to separate answers as needed.)

Step 1 ：Suppose that a polynomial function of degree 5 with rational coefficients has the given numbers as zeros. Find the other zero(s). The given zeros are \(-\frac{1}{3}, \sqrt{5},-3 i\).

Step 2 ：The polynomial function of degree 5 with rational coefficients means that if it has irrational or complex roots, they must come in conjugate pairs. This is due to the fact that when you multiply out \((x - (a + bi))(x - (a - bi))\), the result is a polynomial with rational coefficients.

Step 3 ：Therefore, if the polynomial has a root of \(\sqrt{5}\), it must also have a root of \(-\sqrt{5}\). Similarly, if it has a root of \(-3i\), it must also have a root of \(3i\).

Step 4 ：Final Answer: The other zeros are \(\boxed{-\sqrt{5}, 3i}\)