Answer
The first five terms are $\frac{1}{5}, \frac{-1}{25}, \frac{1}{125}, \frac{-1}{625}$ and $\frac{1}{3125}.$
Work Step by Step
To find the first five terms of $a_n = \frac{(-1)^{n-1}}{5^n}$, we must plug in $n=1, n=2, n=3, n=4$ and $n=5.$
Hence the first five terms are $\frac{1}{5}, \frac{-1}{25}, \frac{1}{125}, \frac{-1}{625}$ and $\frac{1}{3125}.$
