To solve the given logarithmic expression:
We have the logarithmic expression \log_5(\frac{1}{25})=-2 .
This can be rewritten in exponential form as 5^{-2}=\frac{1}{25} .
Since 5^{-2} = \frac{1}{5^2} = \frac{1}{25} ,
\boxed{\frac{1}{25}=\frac{1}{25}} .