ANSWER:
[tex]x=5,-\frac{5}{2}+\frac{5\sqrt[]{3}}{2}i,-\frac{5}{2}-\frac{5\sqrt[]{3}}{2}i[/tex]STEP-BY-STEP EXPLANATION:
We have the following equation:
[tex]\begin{gathered} x^3\: -\: 125\: =0\: \\ x^3\: \: =125\: \end{gathered}[/tex]Solving for x:
[tex]\begin{gathered} x=\sqrt[3]{125} \\ x_1=5 \\ x_2=\sqrt[3]{125}\cdot\frac{-1+\sqrt[]{3}}{2}i=5\cdot\frac{-1+\sqrt[]{3i}}{2}=-\frac{5}{2}+\frac{5\sqrt[]{3}}{2}i \\ x_3=\sqrt[3]{125}\cdot\frac{-1-\sqrt[]{3}}{2}i=5\cdot\frac{-1-\sqrt[]{3i}}{2}=-\frac{5}{2}-\frac{5\sqrt[]{3}}{2}i \end{gathered}[/tex]