1. The problem is to describe the solution set for the inequality $x \leq -2$ or $x > 5$ on a number line ranging from -10 to 10. 2. The inequality $x \leq -2$ means all values of $x$ that are less than or equal to -2. 3. The inequality $x > 5$ means all values of $x$ that are strictly greater than 5. 4. On the number line from -10 to 10, the solution includes all points from -10 up to and including -2, and all points greater than 5 up to 10. 5. This can be written as the union of intervals: $$(-\infty, -2] \cup (5, \infty)$$ but restricted to the visible range $$[-10, 10]$$ it is $$[-10, -2] \cup (5, 10]$$. 6. To graph this, shade the region from -10 to -2 including -2, and from just greater than 5 to 10 including 10. This represents all $x$ values satisfying either $x \leq -2$ or $x > 5$.