Answer
$5a^5+17a^3-a^2-12a-4$
Work Step by Step
Using the Distributive Property, the product of the given expression, $
(a^2+4)(5a^3-3a-1)
,$ is
\begin{array}{l}\require{cancel}
a^2(5a^3)+a^2(-3a)+a^2(-1)+4(5a^3)+4(-3a)+4(-1)
\\\\=
5a^5-3a^3-a^2+20a^3-12a-4
\\\\=
5a^5+(-3a^3+20a^3)-a^2-12a-4
\\\\=
5a^5+17a^3-a^2-12a-4
.\end{array}
