To test this series for convergence

$\displaystyle {\sum_{{{n}={1}}}^{\infty}}\frac{{{n}{3}^{{n}}}}{{{5}{n}^{{3}}+{5}}}$

You could use the Limit Comparison Test, comparing it to the series $\displaystyle {\sum_{{{n}={1}}}^{\infty}}\frac{{b}^{{n}}}{{n}^{{p}}}$ where $\displaystyle {b}$= $\displaystyle {p}$=

Completing the test, it shows the series: