#### Answer

{$13$}

#### Work Step by Step

$\log_{2} (x-5)=3$
$x-5=2^{3}$
$x-5=8$
$x=8+5=13$
Checking the answer by inserting it in the original equation:
$\log_{2} (13-5)=3$
$\log_{2} (8)=3$
$\log_{2} 2^{3}=3$
$\log_{2} 2^{4}=4$
$3\log_{2} 2=3$
$3=3$
Therefore, the solution set is {$13$}.