Answer
$7$
Work Step by Step
Step 1. Rewrite the equation as $log_{5}(x-3)^2=log_{5}(2)+log_{5}(8) \longrightarrow log_{5}(x-3)^2=log_{5}(16)$
Step 2. Thus $(x-3)^2=16\longrightarrow x-3=\pm4\longrightarrow x=-1,7$.
Step 3. Check answers, $x=7$ fits the original equation.