#### Answer

Period$=\frac{1}{2}$ seconds.
Frequency=2 cycles per second.

#### Work Step by Step

The period can be found by first comparing the equation $s(t)=-5\cos 4\pi t$ to $s(t)=a\cos w t$ to find $w$ which is the angular velocity.
By comparing the two equations, we find that $w=4\pi$. Next, we find the period using the formula:
Period$=\frac{2\pi}{w}$
Period$=\frac{2\pi}{4\pi}$
Period$=\frac{1}{2}$ seconds.
Since frequency is the reciprocal of the period, the frequency is 2 cycles per second.