#### Answer

$5$ inches

#### Work Step by Step

The maximum height that the weight rises above its equilibrium position is called the amplitude. It can be found by comparing the equation $s(t)=-5\cos 4\pi t$ to $s(t)=a\cos w t$ where $|a|$ is the amplitude.
Comparing the two equations, we find that $a=5$. Therefore, the maximum height that the weight rises above its equilibrium position (amplitude) is:
$|a|=|-5|=5$ inches