\[5ay^{- 2} \cdot a^{- 4}y^{3} = \frac{5ay^{3}}{y^{2} \cdot a^{4}} =\]
\[= \frac{5a \cdot y^{2} \cdot y}{y^{2} \cdot a \cdot a^{3}} = \frac{5y}{a^{3}}.\]