Answer
$x = -\frac{1}{2}$
Work Step by Step
Rewrite $\frac{1}{5}$ as an exponential expression:
$25^{x} = \frac{1}{5^{1}}$
Since the exponent is in the denominator, rewrite the exponential expression using a negative exponent to get rid of the fraction (use the rule $\frac{1}{a^m}=a^{-m}$):
$25^{x} = 5^{-1}$
Rewrite such that both terms have the same base (note that $25=5^2$):
$(5^{2})^{x} = 5^{-1}$
When raising a power to a power, multiply the exponents, keeping the base as-is (use the rule $\left(a^m\right)^n=a^{mn}$:
$5^{2x} = 5^{-1}$
If two numbers having the same base are equal, that means that their exponents are also the same, so set the exponents equal to one another to solve for $x$:
$2x = -1$
Divide both sides by $2$ to solve for $x$:
$x = -\frac{1}{2}$
