Answer
$x=-1$
Work Step by Step
We are given the equation $5^{x}=.2=\frac{1}{5}$. First, we must write both sides using the same base.
$5^{x}=5^{-1}=\frac{1}{5}$
Next, we must take the natural log of both sides.
$ln(5^{x})=ln(5^{-1})$
$xln(5)=-1ln(5)$
Divide both sides by $ln(5)$.
$x=-1$