Answer
$x=\frac{1}{3}$
Work Step by Step
We rewrite the 125 on the left, so that the base is 5 on both sides.
Left side: $125^x=(5^3)^x$.
By the law of exponents: $(5^3)^x=5^{3x}$
Right side: $5=5^1$
Since both sides have the same base of $5$, they will only be equal if their exponents are also equal.
Equate the exponents to obtain:
$3x=1$
$x=\frac{1}{3}$