#### Answer

$(5m+n)(2+k)$

#### Work Step by Step

$\bf{\text{Solution Outline:}}$
Factor by grouping the first $2$ and the last $2$ terms of the given expression, $
10m+2n+5mk+nk
.$ Then, factor the $GCF$ in each group. Finally, factor the $GCF$ of the entire expression.
$\bf{\text{Solution Details:}}$
Grouping the first $2$ and the last $2$ terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(10m+2n)+(5mk+nk)
.\end{array}
Factoring the $GCF$ in each group, results to
\begin{array}{l}\require{cancel}
2(5m+n)+k(5m+n)
.\end{array}
Factoring the $GCF=
(5m+n)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(5m+n)(2+k)
.\end{array}