Answer
$x=\frac{4}{3}$
Work Step by Step
Note that $125=5^3$.
Write $125$ as $5^3$ to obtain:
$5^{3x-1}=5^3$
RECALL:
If $a^x = a^y$, then $x=y$.
Use the rule above to obtain:
$5^{3x-1}=5^3
\\3x-1=3
\\3x=3+1
\\3x=4
\\x=\frac{4}{3}$