Answer
$x\displaystyle \in\{-\sqrt{5},\ \frac{1}{3}, \ \sqrt{5}\}$
Work Step by Step
Factor in pairs
$x^{2}(3x-1)-5(3x-1)=0$
$(3x-1)(x^{2}-5)=0\qquad$ ... difference of squares
$(3x-1)(x+\sqrt{5})(x-\sqrt{5})=0$
$3x-1=0\ \ \displaystyle \Rightarrow\ \ x=\frac{1}{3}, $
$x\displaystyle \in\{-\sqrt{5},\ \frac{1}{3}, \ \sqrt{5}\}$