Answer
$v = -2.5~cm/s$
Work Step by Step
At $t = 5.0~s$, the particle at $x = 0$ is located at the origin and moving in the negative direction. Thus it is moving at maximum transverse speed which is $v = A~\omega$
We can find the velocity:
$v = -A~\omega$
$v = -(4.0~cm)(0.63~rad/s)$
$v = -2.5~cm/s$
