1. The problem is to find the domain of the function $f(x) = x^2 + 5x + 6$. 2. The domain of a function is the set of all possible input values ($x$) for which the function is defined. 3. Since $f(x)$ is a polynomial function, it is defined for all real numbers. 4. Therefore, the domain of $f(x)$ is all real numbers, which can be written as $(-\infty, \infty)$. Final answer: The domain of $f(x) = x^2 + 5x + 6$ is $\boxed{(-\infty, \infty)}$.