The phases La5Ga3, Gd5Ga3, Y5Ga3, Ho5Ga3 and Er5Ga3 were synthesized from the elements in Ta or by arc melting. La5Ga3 and Y5Ga3 were shown to be line phases. The structures of the first three were established by single-crystal X-ray diffraction refinements to be Ba5Si3 type (P4/ncc), a deformation of the Cr5B3-type structure (I4/mcm) that decreases in magnitude in the order listed. (La5Si3 is also Ba5Si3 type). The structures of the last two listed above were presumed to be the same although the two structure types cannot be distinguished for these elements by Guinier powder diffraction. Samples of Y5Ga3, Ho5Ga3 and Er5Ga3 quenched from about 1175-degrees-C or higher have an evidently slightly deformed Mn5Si3-type Structure which transforms somewhat slowly to the low temperature Ba5Si3 form on annealing at about 800-degrees-C. This transformation has evidently not been seen in prior thermal analysis of these as well as of the analogous Tm, Lu, Sc systems, all of which have been reported to contain only Mn5Si3-type R5Ga3. The law temperature forms of La5Ga3 and Y5Ga3 exhibit Pauli-like paramagnetism and rho273 almost-equal-to 125 muOMEGA cm with metal-like temperature dependences. On the contrary, Mn5Si3-type Y5Ga3 exhibits significantly larger temperature-independent paramagnetism (about 3.5 x 10(-3) e.m.u. mol-1) and rho273 approximately 75 muOMEGA cm with a temperature dependence of 0.07% K-1, so its description as a simple Zintl phase with filled gallium orbitals-valence band is not appropriate. Gd5Ga3 (Ba5Si3) and Ho5Ga3 (low and high temperature types) exhibit Curie-Weiss behavior with mu(eff) almost-equal-to 8.9 mu(B), 10.8 mu(B) and 10.7 mu(B), per lanthanide respectively and metal-like resistivities of 50-100 muOMEGA cm.