The R5Ga3 (R = Sc, Y, Ho, Er, Tm, Lu) phases were prepared by high-temperature solid-state techniques. The structure of monoclinic Sc5Ga3 was determined by single-crystal X-ray diffraction means (C2/m, No. 12, Z = 4, a = 8.0793(5) Angstrom, b = 14.003(1) Angstrom, c 5.9297(3) Angstrom, beta = 90.994(5)degrees), and those of the isotypic R5Ca3, R = Y, Ho, Er, Tm, Lu, were determined by Guinier powder diffraction. The new ScsGa3 structure is a deformation of the hexagonal Mn5Si3 type (P6(3)/mcm) and contains two types of gallium dimers with d(Ga-Ga) = 2.91 and 3.14 Angstrom. The closely spaced Sc1 chains in the parent Mn5Si3 type transform to zigzag chains in concert with displacements of the uniformly spaced gallium atoms to form dimers within distorted confacial square antiprisms of Sc. Matrix effects appear important in the different Ga-2 bond lengths. Electronic calculations reveal that the transformation from the hypothetical Mn5Si3 to the ScsGa3 type is aided by antibonding Ga-Ga interactions between the dimers that are pushed above EF and Ga-Ga and Ga-Sc bonding states just below EF that are stabilized. Sc5Ga3 is appropriately metallic. Except for R = Sc, Lu, the are-melted R5Ga3 compounds above slowly transform on annealing at 1150 degreesC and below into tetragonal Ba5Si3-type structures.