The problem asks to evaluate the exponential function $f(x) = 5^{2x}$ when $x = -1$.

Let’s solve it step-by-step:

1. The function is $f(x) = 5^{2x}$.
2. Plug in $x = -1$ into the function: $f(-1) = 5^{2(-1)} = 5^{-2}$
3. Simplify $5^{-2}$. The negative exponent means the reciprocal: $f(-1) = \frac{1}{5^2} = \frac{1}{25}$

So, the correct answer is $\frac{1}{25}$, which matches the option you selected.

Would you like further details or have any other questions?

Here are 5 related questions you could explore:

1. What is the general rule for simplifying negative exponents?
2. How would the function behave if $x = 0$?
3. What is the value of $f(x)$ when $x = 1$?
4. How do exponential functions compare to linear functions?
5. What happens when the base of an exponential function is less than 1?

Tip: To evaluate exponential functions with negative exponents, always remember that $a^{-n} = \frac{1}{a^n}$.