Another way of looking at this is to visualize $\int_0^\infty c\,dx$, where $c>0$. Now make a drawing, including the $x$-axis, of what this integral...
Each term in the series can be represented by $5+9n,\,0\le n\le240$. In order for a term to be divisible by $5$, $n$ must be divisible by $5$. Hence...