Find the domain of the function $f(x)=\sqrt{\sqrt{x^2-16}-3}$.
\(\sqrt{x^2 - 16} \geq 3\)
\(x^2 - 16 \geq 9\)
\(x^2 \geq 25\)
\(\boxed{x \in (-\infty, -5) \cup (5, \infty)}\)