We are asked to solve the equation $5^{2-x} = \frac{1}{125}$ for $x$.

1. Problem Description

We are asked to solve the equation $5^{2-x} = \frac{1}{125}$ for $x$.

2. Solution Steps

We are given the equation $5^{2-x} = \frac{1}{125}$. We can rewrite $\frac{1}{125}$ as a power of

5. Since $125 = 5^3$, we have $\frac{1}{125} = \frac{1}{5^3} = 5^{-3}$.

Therefore, our equation becomes $5^{2-x} = 5^{-3}$.

Since the bases are equal, we can equate the exponents:

$2 - x = -3$

Now we solve for $x$:

$2 - x = -3$

Subtract 2 from both sides:

$-x = -3 - 2$

$-x = -5$

Multiply both sides by -1:

$x = 5$

3. Final Answer

The solution to the equation $5^{2-x} = \frac{1}{125}$ is $x=5$.