Answer
Continuous everywhere.
Work Step by Step
Recall that if $ f $ is a polynomial function, then we have $\lim_\limits{x\to a}f(x)=f(a)$.
$\lim_\limits{x \to 5^{-}} f(x)= \lim_\limits{x \to 5^{-}} 4x=20$
and $\lim_\limits{x \to 5^{+}} f(x)= \lim_\limits{x \to 5^{+}}(x^2-5)=20$
So, $\lim_\limits{x \to 5^{-}} f(x)= \lim_\limits{x \to 5^{+}}f(x)$ exists.
Now, $\lim_\limits{x \to 5} f(x)=20$
and $ f(5)=20$
so, $\lim_\limits{x \to 5} f(x) = f(5)$
Therefore, the function is continuous everywhere.
