#### Answer

Domain: $(-\infty,\ \infty)$
Range: $[4, \infty)$

#### Work Step by Step

We are given:
$f(x)=5x^{2}+4$
The domain consists of all values that $x$ is allowed to be. In this case, there are no restrictions on $x$, so the domain is all real numbers. Domain: $(-\infty,\ \infty)$.
The range consists of all values that $y$ can be. Since this is a graph of a parabola that starts at $y=4$ and goes up, the range is all real numbers greater than or equal to $4$. Range: $[4, \infty)$.