Answer
$R=5$
and
Interval of convergence is $(-5,5]$
Work Step by Step
Given: $a_n=\frac{x^n}{n5^ n}$
Thus, $\lim\limits_{n \to \infty}|\dfrac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to \infty}|\dfrac{\dfrac{x^{n+1}}{(n+1)5^{n+1}}}{\dfrac{x^n}{n5^ n}}|=\dfrac{|x|}{5}$
Hence,
$R=5$
and
Interval of convergence is $(-5,5]$
