$\log _{25} \frac{1}{5}=$

Step 1 ：The problem is asking for the logarithm base 25 of 1/5. The logarithm base b of a number x is the exponent to which b must be raised to get x. In other words, if \(b^y = x\), then \(\log_b x = y\).

Step 2 ：In this case, we need to find the exponent to which 25 must be raised to get 1/5. We know that \(25^{-1} = 1/25\), so the exponent is likely to be negative.

Step 3 ：We also know that \(25 = 5^2\), so \(25^{-1} = (5^2)^{-1} = 5^{-2}\). Therefore, \(1/5 = 5^{-1}\), so the exponent to which 25 must be raised to get 1/5 is -1/2.

Step 4 ：Thus, \(\log_{25} \frac{1}{5} = -0.5\)

Step 5 ：Final Answer: \(\boxed{-0.5}\)