Answer
$n=16$
Work Step by Step
$a_n=-\frac{5n}{n+8}$ when $a_n=-\frac{10}{3}$
$-\frac{5n}{n+8}=-\frac{10}{3}$
$\implies -\frac{15n}{n+8}=-10$
$\implies -15n=-10(n+8)$
$\implies -15n=-10n-80$
$\implies 15n=10n+80$
$\implies 5n=80$
$\implies n=16$