The general equation for a transverse harmonic wave on a string is given by:

$$ y(x,t) = A \sin(kx - \omega t + \phi) $$

where $A$ is the amplitude of the wave, $k$ is the wave number, $\omega$ is the angular frequency, and $\phi$ is the phase constant. The wave velocity $v$ is related to the wave number and angular frequency by the formula:

$$ v = \frac{\omega}{k} $$

Comparing the given equation with the general equation, we can see that:

$$ A = 5 \, \text{cm} $$

$$ k = 0.003 \, \text{cm}^{-1} $$

$$ \omega = 6 \, \text{rad/s} $$

Therefore, the wave velocity is:

$$ v = \frac{\omega}{k} = \frac{6}{0.003} = 2000 \, \text{cm/s} = \boxed{20 \, \text{m/s}} $$