A many-body expansion of cohesive energy of solid 4He is made up to five-body term, and short-range two-,three-, four- and five-body contributions have been computed by using the Hartree-Fock self-consistent-field technique and the same atomic basis set (6311G). At high densities the Hartree-Fock part of two- and four-body contributions are repulsive, whereas the three- and five-body ones are attractive. The four-body term increases as much as 15% repulsion of two-body term, and at the same time the five-body term reduces 4% of two-body repulsion at 2.5 cm 3 /mol. The four- and five-body terms are found to be important to describe short-range interatomic interaction correctly and to compute the cohesive energy accurately in a wide compression range from 2.5to 7.5 cm3/mol.