hey i m not sure if i did the right if anyone can help
We need to fidn $\displaystyle \lim\left|\frac{a_{n+1}}{a_n}\right|$
So now if $\displaystyle a_{n}=5\cdot 5^{-n}$ then $\displaystyle a_{n+1}={\color{red}5}\cdot 5^{-n+1}$
So your limit is $\displaystyle \lim_{n\to\infty}\frac{5\cdot{5^{-n}}}{5\cdot{5^{-n+1}}}=\frac{1}{5}<1$ thus convergent.