\[\left( - \frac{1}{2}xy^{3} \right)^{3}\left( 4y^{5} \right)^{2} =\]
\[= \left( - \frac{1}{2} \right)^{3}x^{3}y^{9} \cdot 4^{2}y^{10} =\]
\[= - \frac{1}{8} \cdot 16x^{3}y^{9 + 10} = - 2x^{3}y^{19}.\]