\sqrt[3]{5}\cdot \sqrt[3]{20}\cdot \sqrt{20}=(\sqrt{25})^{\frac{1}{3}}\cdot (\sqrt{400})^{\frac{1}{3}}\cdot (\sqrt[3]{8000})^{\frac{1}{2}}=
=(25^{\frac{1}{2}})^{\frac{1}{3}}\cdot (400^{\frac{1}{2}})^{\frac{1}{3}}\cdot (8000^{\frac{1}{3}})^{\frac{1}{2}}=\sqrt[6]{25\cdot 400\cdot 80000}=
=\sqrt[6]{1000\cdot 1000\cdot 80}=\sqrt[6]{10^6\cdot 80}=10\sqrt[6]{80}