To simplify the expression \(\frac{5^{-1}}{5^{-2}}\), we can use the properties of exponents.
When dividing two exponential expressions with the same base, we can subtract the exponents:
\[ \frac{a^m}{a^n} = a^{m-n} \]
Here, we have:
\[ \frac{5^{-1}}{5^{-2}} = 5^{-1 - (-2)} = 5^{-1 + 2} = 5^{1} \]
Now, \(5^{1} = 5\).
None of the provided multiple-choice answers are equivalent to \(5\). However, if the question asked for the reciprocal or an expression that simplifies further, we can express \(5\) in terms of negative exponents too:
To represent \(5\) as a fraction, we recall:
\[ 5 = \frac{5^3}{5^3} = \frac{5^3}{5^2 \cdot 5} = \frac{1}{5^{-1}} \]
But that would be unnecessary here.
Among the provided choices:
- \(\frac{1}{5^3}\)
- \(5^3\)
- \(\frac{1}{5^2}\)
None of them are direct representations of your original fraction after simplification.
The correct answer based on your expression \(\frac{5^{-1}}{5^{-2}} = 5^{1} = 5\) is not present in the options.