Find the domain of the following function. \[ f(x)=\frac{x+5}{x^{2}-16} \] Choose the correct domain below. A. $(-\infty, 16)$ or $(16, \infty)$ B. $(-\infty,-4)$ or $(-4,4)$ or $(4, \infty)$ C. $(-\infty, 5)$ or $(5, \infty)$ D. all real numbers

Step 1 ：The function given is \(f(x)=\frac{x+5}{x^{2}-16}\).

Step 2 ：The domain of a function is the set of all possible input values (x-values) which will output real numbers.

Step 3 ：In this case, the function is a rational function, and the denominator cannot be zero.

Step 4 ：Therefore, we need to find the values of x that make the denominator zero and exclude them from the domain.

Step 5 ：The denominator is \(x^{2}-16\), which can be factored into \((x-4)(x+4)\).

Step 6 ：Therefore, the values of x that make the denominator zero are 4 and -4.

Step 7 ：So, the domain of the function is all real numbers except 4 and -4.

Step 8 ：Final Answer: The correct domain is \(\boxed{(-\infty,-4) \text{ or } (-4,4) \text{ or } (4, \infty)}\).