This work reports an ab initio study of the Ge(111)-5 × 5 reconstruction, which forms on top of a Si(111)-7 × 7 substrate. Detailed descriptions of the structural and electronic properties of this surface, obtained from density-functional calculations, are presented and analyzed. Many similarities with the structural and electronic -electronic properties of related structures such as Si(111)-7 × 7 and Si(111)-5 × 5 were found, in particular the similar localisation properties of the eigenstates around the fermi level, the non-zero density of states at the fermi level, a larger charge density associated with the dangling bonds on the faulted half cell compared with those of the unfaulted half, and the structural relaxations of key surface atoms and bonds, although the magnitudes of these relaxations are somewhat smaller than has been calculated for Si(111)-7 × 7. The calculated charge density distribution is interpreted in terms of population analysis to obtain information on the bonding mechanisms at the surface.