The absence of demixing in the Percus-Yevick theory of fluid mixtures of additive hard-spheres is related to the fact that this theory predicts incorrect virial coefficients B-n for n >3. Incorporation of the exact B-n for 1 less than or equal to n less than or equal to 5 into a rescaled virial expansion is shown instead to lead to demixing for any size asymmetry between the spheres. This demixing is however thermodynamically metastable relative to freezing of the mixture into a partially ordered solid phase. This conclusion is reached on the basis of a density functional estimate of the free-energy of a nonuniform phase in which the large spheres form a face-centered cubic lattice whereas the small spheres remain disordered.