Answer
$x=4$
Work Step by Step
RECALL:
$\log_a{x}=y \longrightarrow a^y = x$
Use the rule above to obtain:
$\log_5{625}=x
\\\longrightarrow 5^x=625$
Note that $625=5^4$. Thus, the expression above is equivalent to:
$5^x=5^4$
Use the rule $a^m=a^n \longrightarrow m=n$ to obtain:
$x=4$