\[4a^{- 5}b \cdot 3a^{2}b^{- 3} = \frac{4b \cdot 3a^{2}}{a^{5}b^{3}} =\]
\[= \frac{4b \cdot 3 \cdot a^{2}}{a^{2} \cdot a^{3} \cdot b{\cdot b}^{2}} = \frac{12}{a^{3}b^{2}}\]