You almost certainly meant to say the particle's position is a function of time t, not some other variable x (or vice versa) so that
s(t) = 5t sin(2t)
Differentiate s(t) to get the instantaneous velocity of the particle at time t. By the product rule,
s'(t) = 5 sin(2t) + 10t cos(2t)
Evaluate the derivative at t = 0 :
s'(0) = 0
