1. The problem asks to find the domain of the function $$g(x) = \frac{5x}{x - 5}$$. 2. The domain of a function includes all real numbers except those that make the denominator zero, because division by zero is undefined. 3. Set the denominator equal to zero and solve for $$x$$: $$x - 5 = 0$$ $$x = 5$$ 4. Since $$x = 5$$ makes the denominator zero, $$x = 5$$ is excluded from the domain. 5. Therefore, the domain is all real numbers except $$5$$, which in interval notation is: $$(-\infty, 5) \cup (5, \infty)$$