If you have $\sum_{n = 0}^\infty(4/5)^n$ and you are asked to represent it as a geometric series you would:
$\sum_{n = 0}^\infty(4/5)(4/5)^{n-1}$ //factor out your constant
therefore $a = 4/5$, $r = 4/5$, $|r| < 1$ checks out.
Using $a / (1 - r)$ you get $(4/5)/(1 - 4/5)$
$(4/5)/(1/5) = 4$. which confuses me because the solution said the answer was $5$?