$(a)$ Find the open interval $of$ convergence $of$ the power series

${\displaystyle \underset{n=3}{\overset{}{}}}\frac{n}{(2n+1)5^n}(x-3{)}^{2n+1}$

$(b)$ Does the series converge $at$ the left endpoint $of$ the open interval $of$ convergence?

Justify your answer.