Answer
$x=32$
Work Step by Step
RECALL:
$\log_b{x}=y \longrightarrow b^y=x$
Write the equation in exponential form using the rule above to obtain:
$5^2=x-7
\\25=x-7$
Solve for $x$ to obtain:
$\begin{array}{ccc}
&25 &= &x-7
\\&25+7&=&x-7+7
\\&32&=&x\end{array}$