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I'm not sure why you say it isn't? It still applies but a moving charge may also experience a magnetic force so coulomb's law on its own would ignore that. The Lorentz force equation includes both electric and magnetic forces when calculating force on a moving charge:
F = q(E + v x B)
Coulomb's law deals with static charges and their interaction with the environment around them. This is usually referred to as the inverse square law of electrostatics. This implies that the charges under consideration are static, i.e their position is fixed and only then the force follows coulomb's statements and conclusions. Also, the great Maxwell has proved it beyond doubt that every moving charge creates an electrical field and also a magnetic field around it. This further results in action reaction pair which hampers the dynamics of a charge in motion. The created magnetic field would then apply force perpendicular to both the field and the velocity vectors on the charge forcing it to follow a helical sort of path.
The force is thus both electrical and as well due to the magnetic field generated by the moving charge which is given by the Lorentz force equation.
F = q.E + q.VxB