Convert to a logarithmic equation. \[ 5^{-3}=\frac{1}{125} \]

Step 1 ：Given the equation in exponential form: \(5^{-3} = \frac{1}{125}\)

Step 2 ：We can convert this to logarithmic form. The relationship between exponential and logarithmic forms is as follows: if \(b^y = x\), then \(\log_b(x) = y\). Here, \(b\) is the base, \(y\) is the exponent, and \(x\) is the result.

Step 3 ：In this case, the base \(b\) is 5, the exponent \(y\) is -3, and the result \(x\) is \(\frac{1}{125}\).

Step 4 ：Substituting these values into the logarithmic form, we get \(\log_5\left(\frac{1}{125}\right) = -3\).

Step 5 ：\(\boxed{\log_{5}\left(\frac{1}{125}\right) = -3}\) is the final answer.