Answer
$ln5-\sum_{n=1}^{\infty}\frac{x^{n}}{5^{n}n}$
$R=5$
Work Step by Step
$f(x)=ln(5-x)=ln5-\sum_{n=0}^{\infty}\frac{x^{n+1}}{5^{n+1}n+1}=ln5-\sum_{n=1}^{\infty}\frac{x^{n}}{5^{n}n}$
$\lim\limits_{n \to \infty}|\frac{a_{n+1}}{a_{n}}|=\lim\limits_{n \to \infty}|\dfrac{\frac{x^{(n+1)+1}}{5^{n+1}n+1}}{\frac{x^{n+1}}{5^{(n+1)+1}(n+1)+1}}|$
$=|\frac{x}{5}|\lt 1$
The given series converges with $R=5$
