1. The problem is to solve the compound inequality $-2x > -5 > -15$. 2. Compound inequalities can be split into two separate inequalities: $-2x > -5$ and $-5 > -15$. 3. The inequality $-5 > -15$ is always true, so we focus on solving $-2x > -5$. 4. To solve $-2x > -5$, divide both sides by $-2$. Remember, dividing by a negative number reverses the inequality sign. 5. Dividing, we get $x < \frac{-5}{-2} = \frac{5}{2}$. 6. Therefore, the solution to the compound inequality is $x < \frac{5}{2}$. 7. In plain language, $x$ must be less than $2.5$ for the inequality to hold true.