Answer
$(x+5)(x+3)$
Work Step by Step
Factoring the $GCF=
(x+5)
,$ the given expression, $
x(x+5)+3(x+5)
,$ is equivalent to
\begin{array}{l}\require{cancel}
(x+5)
\left[
\dfrac{x(x+5)}{(x+5)}+\dfrac{3(x+5)}{(x+5)}
\right]
\\\\=
(x+5)
\left[
\dfrac{x\cancel{(x+5)}}{\cancel{(x+5)}}+\dfrac{3\cancel{(x+5)}}{\cancel{(x+5)}}
\right]
\\\\=
(x+5)(x+3)
.\end{array}