A fifth order finite difference alternative weighted essentially non-oscillatory scheme is studied for a five-equation model, which plays an important role in the modelling of compressible multi-component flows. In our algorithm, the primitive variables are used in the weighted essentially non-oscillatory interpolation, from which it can be proved that the equilibriums of the velocity and pressure are preserved respectively throughout the whole computation of contact moving interface problems, under the ideal and stiffened gases equations of state. In addition, it is found that with the interpolation being performed on the characteristic variables which are the projections of the primitive variables, non-physical oscillations appearing around the contact waves can be significantly restrained. Numerical examples verify the theory and illustrate the robustness of the proposed scheme.