Recall that for an infinite geometric series of the form
[tex]\displaystyle\sum_{n=0}^\infty ar^n[/tex]
as long as [tex]|r|<1[/tex], the series converges to the value [tex]\dfrac{a}{1-r}[/tex].
Here you have [tex]r=-\dfrac23[/tex], so the series converges. You have
[tex]\displaystyle\sum_{n=0}^\infty 5\left(-\dfrac23\right)^n=\dfrac5{1-\left(-\dfrac23\right)}=3[/tex]
