(5) Let $P_{o}(x)=x^{3}+313 x^{2}-77 x-8$, for integers $n \geqslant 1$ define $P_{n}(x)=P_{n-1}(x-n)$, then the coefficient of the $x$ term in $P_{20}(x)$ is
(5) 763 Prompt:
$$
\begin{aligned}
P_{20}(x) & =P_{19}(x-20)=P_{18}(x-20-19)=P_{17}(x-20-19-18) \\
& =\cdots=P_{0}(x-20-19-\cdots-2-1)=P_{0}(x-210) \\
& =(x-210)^{3}+313(x-210)^{2}-77(x-210)-8 .
\end{aligned}
$$

The coefficient of the $x$ term is
$$
3 \times 210^{2}-313 \times 2 \times 210-77=763 .
$$