Answer
$x=7$
Work Step by Step
Let
$\log_{5}{5^7} = x$
RECALL:
$\log_b{y} =x \longrightarrow b^x=y$
Use the rule above, where $y=5^7$ and $b=5$, to obtain:
$5^x=5^7$
Use the rule "If $a^x=a^y$, then $x=y$" to obtain:
$x=7$