#### Answer

$x=\pm 3$

#### Work Step by Step

$\log _{5}\left( x+2\right) +\log _{5}\left( x-2\right) =1\Rightarrow \log _{5}\left( \left( x+2\right) \left( x-2\right) \right) =\log _{5}5$
$\Rightarrow \left( x+2\right) \left( x-2\right) =5\Rightarrow x^{2}-4=5\Rightarrow x^{2}=9\Rightarrow x=\pm 3$