Answer
$(r+2)(5r+13)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the given expression,
\begin{align*}
5r^2+23r+26
\end{align*}
has $ac=
5(26)=130
$ and $b=
23
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
10,13
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{align*}
5r^2+10r+13r+26
\end{align*}
Grouping the first and second terms and the third and fourth terms, the expression above is equivalent to
\begin{align*}
(5r^2+10r)+(13r+26)
\end{align*}
Factoring the $GCF$ in each group results to
\begin{align*}
5r(r+2)+13(r+2)
\end{align*}
Factoring the $GCF=
(r+2)
$ of the entire expression above results to
\begin{align*}
(r+2)(5r+13)
\end{align*}
