Using the recurrence, you should get it as $O(n)$.
After $k$ iterations, this is what the recurrence would look like:
$T(n) = T((\frac{4}{5})^k n) + cn(1 + 4/5 + 16/25 + \dots + (\frac{4}{5})^k)$
$\,\,\,\,\,\,\,\,\,\,\,\, \,\,\,\leq T((\frac{4}{5})^k n) + cn(1 + 4/5 + 16/25 + \dots \infty)$
which is an infinite GP with $a = 1$ and $d = 4/5$.
Therefore, your recurrence becomes:
$T(n) = 1 + 5cn$ which is $O(n)$