Answer
$\log_{5}{\left(\frac{1}{125}\right)}=-3$
Work Step by Step
We are given:
$5^{-3}=\frac{1}{125}$
Recall the definition of a logarithm (pg. 451):
$\log_{b}{x}=y$ iff $b^y=x$
Applying this definition to our equation ($x=1/125, b=5, y=-3$), we get:
$\log_{5}{\left(\frac{1}{125}\right)}=-3$