\[\left( - 1\frac{2}{3}xy^{5} \right)^{2} \cdot 5\frac{2}{5}x^{3}y^{10} =\]
\[= \left( - \frac{5}{3} \right)^{2} \cdot \frac{27}{5} \cdot x^{2}y^{10} \cdot x^{3}y^{10} =\]
\[= \frac{25}{9} \cdot \frac{27}{5}x^{5}y^{20} = 5 \cdot 3 \cdot x^{5}y^{20} = 15x^{5}y^{20}\]