Answer
$\infty$
Work Step by Step
We need to apply ratio test for a given series.
$\lim\limits_{n \to \infty} |\dfrac{a_{n+1}}{a_n}|=\lim\limits_{n \to \infty} |\dfrac{5^{n+1}}{(n+1)!} \times \dfrac{n!}{5^n}|=\lim\limits_{n \to \infty} \dfrac{5}{n+1}=0$
This implies that the radius of convergence of the series is $\infty$ and the series converges at $R$.
