Answer
-1
Work Step by Step
From the definition of the logarithmic function on page 456, we know that $y=log_{b}x$ is equivalent to $b^{y}=x$(for $x\gt0$, $b\gt0$, and $b\ne1$).
Therefore, $log_{5}\frac{1}{5}=-1$, because $5^{-1}=\frac{1}{5}$.