#### Answer

$(-\infty, -3) \cup (-2, +\infty)$
Refer to the image below for the graph.

#### Work Step by Step

Factor the trinomial to obtain:
$(x+2)(x+3)\gt 0$
Next, find the zeros of each factor.
To find value/s of $x$ that will make each factor equal to zero, equate each factor to zero then solve each equation:
$\begin{array}{ccc}
&x+2=0 &\text{ or } &x+3=0
\\&x=-2 &\text{ or } &x=-3
\end{array}$
Next step is to find the intervals.
The zeros $-3$ and $-2$ divide the number line into three intervals, namely:
$(-\infty, -3), (-3, -2), \text{ and } (-2, +\infty)$.
$\bf\text{Make a table of signs}.$
(refer to the attached image below)
$\bf\text{Solve}$
From the table of signs, it can be seen that $(x+2)(x+3)\gt 0$, which is equivalent to $x^2+5x+6\gt 0$, in the intervals $(-\infty, -3)$ and $(-2, +\infty)$.
The inequality involves strictly $\gt$ therefore the endpoints $-3$ and $-2$ are not part of the solution set.
Thus, the solution set is:
$(-\infty, -3) \cup (-2, +\infty)$.
To graph this, plot holes (or hollow dots) at $-3$ and $-2$ then shade the region to the left of $-3$ and to the right of $-2$.
(refer to the attached image in the answer part above)