Answer
$(-5,-2)$
Work Step by Step
Step 1. Based the inequality $\frac{x+5}{x+2}\lt0$, the boundary points are $x=-5,-2$
Step 2. Using the test points to examine signs across the boundary points, we have
$...(+)...(-5)...(-)...(-2)...(+)...$
Thus the solutions are $-5\lt x\lt-2$
Step 3. We can express the solutions on a real number line as shown in the figure.
Step 4. We can express the solutions in interval notation as $(-5,-2)$
