#### Answer

$x_{1}=0,x_{2}=\dfrac {8}{3}$

#### Work Step by Step

$\log _{5}\left[ \left( 3x+5\right) \left( x+1\right) \right] =1\Rightarrow \left( 3x+5\right) \left( x+1\right) =5^{1}$
$\Rightarrow 3x^{2}+8x+5=5\Rightarrow 3x^{2}+8x=0\Rightarrow 3x^{2}=8x\Rightarrow x_{1}=0,x_{2}=\dfrac {8}{3}$