Consider the function

$f(x)= \begin{cases}\frac{P(x)}{\sin (x-2)}, & x \neq 2 \\ 7, & x=2\end{cases}$

$P^{\prime \prime}(x)=$ const. $\Rightarrow P(x)$ is a 2 degree polynomial

$f(x)$ is cont. at $x=2$

$f\left(2^{+}\right)=f\left(2^{-}\right)$

$\lim _{x \rightarrow 2^{+}} \frac{P(x)}{\sin (x-2)}=7$

$\lim _{x \rightarrow 2^{+}} \frac{(x-2)(a x+b)}{\sin (x-2)}=7 \Rightarrow 2 a+b=7$

$P(x)=(x-2)(a x+b)$

$\mathrm{P}(3)=(3-2)(3 \mathrm{a}+\mathrm{b})=9 \Rightarrow 3 \mathrm{a}+\mathrm{b}=9$

$a=2, b=3$

$P(5)=(5-2)(2.5+3)=3.13=39$