Answer
$-3$
Work Step by Step
$\left( \sqrt [3] {5}\right) ^{-x}=\left( \dfrac {1}{5}\right) ^{x+2}\Rightarrow \left( 5^{\dfrac {1}{3}}\right) ^{-x}=\left( 5^{-1}\right) ^{x+2}\Rightarrow 5^{-\dfrac {x}{3}}=5^{-\left( x+2\right) }\Rightarrow -\dfrac {x}{3}=-\left( x+2\right) \Rightarrow \dfrac {2x}{3}=-2\Rightarrow x=-3$