5. Let $x, y, z$ be the roots of the equation $t^{3}-5 t-3=0$. Find $x^{3} y^{3}+x^{3} z^{3}+y^{3} z^{3}$.
Solution. The polynomial has 3 different real roots, since $\mathrm{P}(-100)0, \mathrm{P}(0)0$. By Vieta's theorem, $\mathrm{x}+\mathrm{y}+\mathrm{z}=0, \mathrm{xy}+\mathrm{xz}+\mathrm{yz}=-5, \mathrm{xyz}=3$.

$$
\begin{gathered}
x^{3} y^{3}+x^{3} z^{3}+y^{3} z^{3}=(5 x+3)(5 y+3)+(5 x+3)(5 z+3)+(5 y+3)(5 z+3) \\
=25(x y+x z+y z)+30(x+y+z)+27=-98
\end{gathered}
$$

Answer: -98.