Answer
$10a^{3}(a^{2}-a-6)$
Work Step by Step
$10a^{5}-10a^{4}-60a^{3}$
The prime factorization of $10a^{5}$ is $[2\cdot 5\cdot a\cdot a\cdot a]\cdot a\cdot a$
The prime factorization of $10a^{4}$ is $[2\cdot 5\cdot a\cdot a\cdot a]\cdot a$
The prime factorization of $60a^{3}$ is$ [2]\cdot 2\cdot 3\cdot[5\cdot a\cdot a\cdot a]$
The largest common factor is $2\cdot 5\cdot a\cdot a\cdot a=10a^{3}$
Factor out $10a^{3}$ from the given expression.
$=10a^{3}(a^{2}-a-6)$