#### Answer

Divergent

#### Work Step by Step

In order to solve this problem we will take the help of the Integral Test.
Then we have $\int_{1}{n} \dfrac{5}{x+1}dx=5 (\ln (n+1))-5 (\ln 2)$
and $\int_{1}({\infty}) (\dfrac{5}{x+1})dx=\infty$
Thus, the series is divergent.