Answer
$x^3+3x^2+7x+10$
Work Step by Step
Using the Distributive Property, the given expression, $
(x+2)(x^2+x+5)
,$ is equivalent to
\begin{array}{l}\require{cancel}
x(x^2)+x(x)+x(5)+2(x^2)+2(x)+2(5)
\\\\=
x^3+x^2+5x+2x^2+2x+10
\\\\=
x^3+(x^2+2x^2)+(5x+2x)+10
\\\\=
x^3+3x^2+7x+10
.\end{array}