5. Among the following equations, the polynomial equation that has $\sqrt[3]{5}-\sqrt{2}$ as a root is ( ).
(A) $x^{6}-6 x^{4}+9 x^{3}-60 x-7=0$
(B) $x^{6}+6 x^{4}-10 x^{3}-60 x-7=0$
(C) $x^{6}-6 x^{4}-9 x^{3}-60 x+7=0$
(D) $x^{6}-6 x^{4}-10 x^{3}-60 x+7=0$
5. D.

From the problem, we know
$$
\begin{array}{l}
x=\sqrt[3]{5}-\sqrt{2} \Rightarrow x+\sqrt{2}=\sqrt[3]{5} \\
\Rightarrow x^{3}+3 \sqrt{2} x^{2}+6 x+3 \sqrt{2}=5 \\
\Rightarrow\left(x^{3}+6 x-5\right)^{2}=\left(-3 \sqrt{2} x^{2}-3 \sqrt{2}\right)^{2} \\
\Rightarrow x^{6}-6 x^{4}-10 x^{3}-60 x+7=0 .
\end{array}
$$