Answer
$(x-4)(5x+1)$
Work Step by Step
Using the factoring of trinomials in the form $ax^2+bx+c,$ the $\text{
expression
}$
\begin{array}{l}\require{cancel}
5x^2-19x-4
\end{array} has $ac=
5(-4)=-20
$ and $b=
-19
.$
The two numbers with a product of $c$ and a sum of $b$ are $\left\{
-20,1
\right\}.$ Using these $2$ numbers to decompose the middle term of the trinomial expression above results to
\begin{array}{l}\require{cancel}
5x^2-20x+1x-4
.\end{array}
Grouping the first and second terms and the third and fourth terms, the given expression is equivalent to
\begin{array}{l}\require{cancel}
(5x^2-20x)+(x-4)
.\end{array}
Factoring the $GCF$ in each group results to
\begin{array}{l}\require{cancel}
5x(x-4)+(x-4)
.\end{array}
Factoring the $GCF=
(x-4)
$ of the entire expression above results to
\begin{array}{l}\require{cancel}
(x-4)(5x+1)
.\end{array}