Both a free volume approach for Helmholtz free energy and theoretically based fitted formulas for a radial distribution function of hard-sphere solid are combined to describe the Helmholtz free energy of a solid phase with the hard-core attractive Yukawa (HCAY) potential in the framework of first-order thermodynamic perturbation theory. The corresponding Helmholtz free energy of the fluid phase is calculated from a recently proposed analytical expression based on the inverse temperature expansion and mean spherical approximation. The predicted solid-liquid phase transition for the HCAY system is in far better agreement with simulation than a previous perturbation weighted density approximation. The present formalism is employed as a predictor of protein solidification and metastable liquid-liquid coexistence of crystallizing protein solution, in satisfactory agreement with the available experimental data.