Answer
$(-\infty,-5)\cup(2,\infty)$
Work Step by Step
Step 1. Based the inequality $\frac{x+5}{x-2}\gt0$, the boundary points are $x=-5,2$
Step 2. Using test points to examine signs across the boundary points, we have
$...(+)...(-5)...(-)...(2)...(+)...$
Thus the solutions are $x\lt-5$ or $x\gt2$
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 $(-\infty,-5)\cup(2,\infty)$
