1. **State the problem:** Find the domain and range of the function $$f(x) = x^3 + 5$$. 2. **Determine the domain:** The domain of a function is the set of all possible input values ($x$) for which the function is defined. Since $f(x) = x^3 + 5$ is a polynomial function, it is defined for all real numbers. Therefore, the domain is $$\text{Domain} = (-\infty, \infty)$$. 3. **Determine the range:** The range is the set of all possible output values ($f(x)$). The cubic function $x^3$ can take on all real values from $-\infty$ to $\infty$. Adding 5 shifts the graph vertically. Thus, the range is also all real numbers: $$\text{Range} = (-\infty, \infty)$$. **Final answer:** Domain: $(-\infty, \infty)$ Range: $(-\infty, \infty)$