#### Answer

$\color{blue}{(-\infty, -5) \cup (-5, +\infty)}$

#### Work Step by Step

RECALL:
The domain of the sum, difference, and product of $f(x)$ and $g(x)$ is the common elements of the domains of the two functions.
The domain of the respective functions are:
$f(x)$ is defined for all real numbers except $-5$ (since 5 will make the denominator zero) so its domain is: $(-\infty, 5) \cup (5, +\infty)$
$g(x)$ is defined for all real numbers so its domain is: $(-\infty, +\infty)$
Note that:
$[(-\infty, -5) \cup(-5, +\infty)] \cap (-\infty, +\infty)
\\= (-\infty, -5) \cup (-5, +\infty)$.
Thus, the domain of the sum, difference, and product of $f(x)$ and $g(x)$ is:
$\color{blue}{(-\infty, -5) \cup (-5, +\infty)}$