Let

$a_n=\frac{5n}{12n+15}.$

For the following answer blanks, decide whether the given sequence or series is convergent or divergent. If convergent, enter the limit $($for a

sequence$)$ or the sum $($for a series$).$ If divergent, enter 'infinity' if it diverges to $,\text{'}-$infinity' if it diverges to $-$ or 'DNE' otherwise.

$($a$)$ The series ${\displaystyle \underset{n=1}{\overset{}{}}}\frac{5n}{12n+15}.$

$($b$)$ The sequence $\{\frac{5n}{12n+15}\}.$