$$A=x^{5}-1; B=y^{3}+2^{3}$$
$x=\sqrt[5]{A+1}\text{, }y=\sqrt[3]{B-8}$
$x=\sqrt[5]{A+1}\text{, }y=e^{\frac{2\pi i}{3}}\sqrt[3]{B-8}$
$x=\sqrt[5]{A+1}\text{, }y=e^{\frac{4\pi i}{3}}\sqrt[3]{B-8}$
$x=e^{\frac{2\pi i}{5}}\sqrt[5]{A+1}\text{, }y=\sqrt[3]{B-8}$
$x=e^{\frac{2\pi i}{5}}\sqrt[5]{A+1}\text{, }y=e^{\frac{2\pi i}{3}}\sqrt[3]{B-8}$
$x=e^{\frac{2\pi i}{5}}\sqrt[5]{A+1}\text{, }y=e^{\frac{4\pi i}{3}}\sqrt[3]{B-8}$
$x=e^{\frac{4\pi i}{5}}\sqrt[5]{A+1}\text{, }y=\sqrt[3]{B-8}$
$x=e^{\frac{4\pi i}{5}}\sqrt[5]{A+1}\text{, }y=e^{\frac{2\pi i}{3}}\sqrt[3]{B-8}$
$x=e^{\frac{4\pi i}{5}}\sqrt[5]{A+1}\text{, }y=e^{\frac{4\pi i}{3}}\sqrt[3]{B-8}$
$x=e^{\frac{6\pi i}{5}}\sqrt[5]{A+1}\text{, }y=\sqrt[3]{B-8}$
$x=e^{\frac{6\pi i}{5}}\sqrt[5]{A+1}\text{, }y=e^{\frac{2\pi i}{3}}\sqrt[3]{B-8}$
$x=e^{\frac{6\pi i}{5}}\sqrt[5]{A+1}\text{, }y=e^{\frac{4\pi i}{3}}\sqrt[3]{B-8}$
$x=e^{\frac{8\pi i}{5}}\sqrt[5]{A+1}\text{, }y=\sqrt[3]{B-8}$
$x=e^{\frac{8\pi i}{5}}\sqrt[5]{A+1}\text{, }y=e^{\frac{2\pi i}{3}}\sqrt[3]{B-8}$
$x=e^{\frac{8\pi i}{5}}\sqrt[5]{A+1}\text{, }y=e^{\frac{4\pi i}{3}}\sqrt[3]{B-8}$
$x=\sqrt[5]{A+1}$
$y=\sqrt[3]{B-8}$