For the following polynomial function, find all zeros and their multiplicities.
\[
f(x)=(x-5)^{3}\left(x^{2}-2\right)
\]
Choose the correct answer below.
A. 5 (multiplicity 3 ) $\sqrt{2},-\sqrt{2}$
B. -5 (multiplicity 3 ) $, \sqrt{2},-\sqrt{2}$
C. 2 (multiplicity 2 ) $\sqrt{5},-\sqrt{5}$
D. -2 (multiplicity 2$), \sqrt{5},-\sqrt{5}$

Step 1 ：We are given the polynomial function \(f(x)=(x-5)^{3}(x^{2}-2)\). We need to find all zeros of this function and their multiplicities.

Step 2 ：To find the zeros of the polynomial, we set the polynomial equal to zero and solve for x. These solutions can be real or complex numbers.

Step 3 ：Setting each factor equal to zero, we find that the roots of the polynomial are \(5\), \(\sqrt{2}\), and \(-\sqrt{2}\).

Step 4 ：We also observe that the root \(5\) is repeated three times, indicating that its multiplicity is 3.

Step 5 ：Final Answer: The zeros of the polynomial are \(\boxed{5, \sqrt{2}, -\sqrt{2}}\). The zero \(5\) has a multiplicity of 3.