Question 150
Let $x_{1}, x_{2}, \ldots, x_{n}$ be a sequence in which each term is $0$, $1$ or $-2$. If $$
\left\{
\begin{array}{l}
x_{1}+x_{2}+\cdots+x_{n}=-5 \\
x_{1}^{2}+x_{2}^{2}+\cdots+x_{n}^{2}=19
\end{array}
\right.
$$ determine $x_{1}^{5}+x_{2}^{5}+\cdots+x_{n}^{5}$.
\left\{
\begin{array}{l}
x_{1}+x_{2}+\cdots+x_{n}=-5 \\
x_{1}^{2}+x_{2}^{2}+\cdots+x_{n}^{2}=19
\end{array}
\right.
$$ determine $x_{1}^{5}+x_{2}^{5}+\cdots+x_{n}^{5}$.