Answer
Absolutely Convergent
Work Step by Step
A series $ \Sigma a_n$ is defined as absolutely convergent when the series $ \Sigma |a_n|$ is convergent.
From the series, we notice that $ \Sigma_{n=1}^{\infty} |(-5)^{-n}|= \Sigma_{n=1}^{\infty} 5^{-n}$
This suggests a geometric series with common ratio $r=\dfrac{1}{5} \lt 1$
Remember that a geometric series is said to be convergent when the common ratio $|r| \lt 1$.
This implies that the series is Absolutely Convergent.