Answer
$\color{blue}{(-\infty, -5) \cup (-1, +\infty)}$
Work Step by Step
Solve the related equation $(x+1)(x+5)=0$.
Use the Zero Factor Property by equating each factor to zero, then solve each equation to obtain:
\begin{array}{ccc}
&x+1 &\text{or} &x+5=0
\\&x=-1 &\text{or} &x=-5
\end{array}
The numbers $-1$ and $-5$ divide the number line into three regions, namely:
A $(-\infty, -5)$
B $(-5, -1)$
C $(-1, +\infty)$
Pick a test point value in each region and substitute it into the given inequality. If the test point satisfies the given inequality, then the region where the test point value belongs is a solution. (Refer to the table below.)
Thus, the solution includes the intervals $(-\infty, -5)$ and $(-1, +\infty)$.
The numbers $-5$ and $-1$ are not included in the solution because the inequality symbol involved is $\gt$.
Therefore, the solution is:
$\color{blue}{(-\infty, -5) \cup (-1, +\infty)}$
