Answer
The series is divergent.
Work Step by Step
An infinite geometric series is a series of the form
$ a+ar+ar^{2}+ar^{3}+\cdots+ar^{n-1}+\cdots$
An infinite geometric series for which $|r| < 1$
has the sum $S=\displaystyle \frac{a}{1-r}$
If $|r| \geq 1$, the series diverges (the sum does not exist).
------------
$a=5$
$r=\displaystyle \frac{-5(1.01}{5}=-1.01, \quad |r| > 1,$
so the series is divergent.
