Answer
$(a-3)(a+8)$
Work Step by Step
Let $z=(a+5)$. Then the given expression, $
(a+5)^2-5(a+5)-24
$, is equivalent to $
z^2-5z-24
$.
The two numbers whose product is $ac=
1(-24)=-24
$ and whose sum is $b=
-5
$ are $\{
-8,3
\}$. Using these two numbers to decompose the middle term, then the factored form of the expression, $
z^2-5z-24
$, is
\begin{array}{l}\require{cancel}
z^2-8z+3z-24
\\\\=
(z^2-8z)+(3z-24)
\\\\=
z(z-8)+3(z-8)
\\\\=
(z-8)(z+3)
.\end{array}
Since $z=(a+5)$, then,
\begin{array}{l}
(a+5-8)(a+5+3)
\\\\=
(a-3)(a+8)
.\end{array}
