Correct. If $\displaystyle{5}+{\sqrt[{{3}}]{{{x}-{2}}}}={8}\usepackage{cmbright}\Huge\$ , then $\displaystyle{\sqrt[{{3}}]{{{x}-{2}}}}={3}\usepackage{cmbright}\Huge\$ , so $\displaystyle{{\left({\sqrt[{{3}}]{{{x}-{2}}}}\right)}}^{{3}}={{\left({3}\right)}}^{{3}}\usepackage{cmbright}\Huge\$ . Then $\displaystyle{x}-{2}={27}\usepackage{cmbright}\Huge\$ , so $\displaystyle{x}={29}\usepackage{cmbright}\Huge\$ .