Step 1 :The equation is asking for the exponent that when applied to 5 will result in 1/125.
Step 2 :This is equivalent to asking for the exponent that when applied to 5 will result in \(5^{-3}\), since 1/125 is the same as \(5^{-3}\).
Step 3 :Therefore, the exponent we are looking for is -3.
Step 4 :The exponent calculated is -3.0000000000000004, which is very close to -3. The slight difference is due to the precision limit of floating point numbers.
Step 5 :Therefore, we can conclude that the exponent is -3.
Step 6 :Final Answer: \(\boxed{-3}\)