Answer
$=x^{5}+x^{6}+\frac{x^7}{2!}+...+\frac{x^{n+5}}{n!}+...$
Work Step by Step
We are given $f(x)=x^{5}e^{x}$
with $c=x^{5}$ for $r$ in $(-\infty,\infty)$
The Taylor series for $f(x)=x^{5}e^{x}$ is
$f(x)=x^{5}.1+x^{5}.x+x^{5}\frac{1}{2!}x^{2}+...+\frac{1}{n!}x^n+...$
$=x^{5}+x^{6}+\frac{x^7}{2!}+...+\frac{x^{n+5}}{n!}+...$
