Answer
$(-\infty, -4] \cup [5, +\infty)$
Refer to the image below for the graph.
Work Step by Step
First step is to find the zeros of each factor.
The factors $x-5$ and $x+4$ are zero when $x=5$ and $x=-4$, respectively.
Next step is to find the intervals.
The zeros $-4$ and $5$ divide the number line into three intervals, namely:
$(-\infty, -4), (-4, 5), \text{ and } (5, +\infty)$.
$\bf\text{Make a table of signs}.$
(refer to the attached image below)
$\bf\text{Solve}$
From the table of signs, it can be seen that $(x-5)(x+4)\ge 0$ in the intervals $(-\infty, -4)$ and $(5, +\infty)$.
The inequality involves $ge$ therefore the endpoints $-4$ and $5$ are part of the solution set.
Thus, the solution set is $(-\infty, -4] \cup [5, +\infty)$.
To graph this, plot holes at $-4$ and $5$ then shade the region to the left of $-4$ and the region to the right of 5.
(refer to the attached image in the answer part above)
