To solve a rational inequality with a constant numerator, such as $\frac{5}{x^2 - 2x - 15} > 0$, first verify it is in the correct form with $0$ on one side. Factoring the denominator yields $\frac{5}{(x + 3)(x - 5)} > 0$. Next, determine the zero partition numbers. The quotient is $0$ when the numerator is $0$; however, since the numerator is the constant $5$, the quotient cannot be $0$. Thus, there are no zero partition numbers from the numerator. The quotient is undefined when the denominator is $0$, which happens when $(x + 3)(x - 5) = 0$, resulting in $x = -3$ and $x = 5$. These are the only zero partition numbers. Use $-3$ and $5$ to divide the number line into intervals: $(-\infty, -3)$, $(-3, 5)$, and $(5, \infty)$. By testing values in each interval, we find where the quotient is positive. Because the inequality is strictly greater than $0$, the zero partition numbers are excluded. The final solution in interval notation is $(-\infty, -3) \cup (5, \infty)$.