The syntheses and distributions of binary R(5)Pn(3) phases among the hexagonal Mn5Si3 (M), and the very similar orthorhombic beta-Yb5Sb3 (Y) and Y5Bi3 (YB) structure types have been studied for R = Y, Gd-Lu and Pn = Sb, Bi. Literature reports of M and YB-type structure distributions among R5Pn3 phases, R = Y, Gd-Ho, are generally confirmed. The reported M-type Er5Sb3 could not be reproduced. Alternate stabilization of Y-type structures by interstitials H or F has been disproved for these nominally trivalent metal pnictides. Single crystal structures are reported for (a) the low temperature YB form of Er5Sb3 (Pnma, a = 7.9646(9) angstrom, b = 9.176(1) angstrom, c = 11.662(1) angstrom), (b) the YB- and high temperature Y-types of Tm5Sb3 (both Pnma, a = 7.9262(5), 11.6034(5) angstrom, b = 9.1375(6), 9.1077(4) angstrom, c = 11.6013(7), 7.9841(4) angstrom, respectively), and (c) the YB structure of Lu5Sb3, a = 7.8847(4) angstrom, b = 9.0770(5) angstrom, c = 11.5055(6) angstrom. Reversible, temperature-driven phase transitions (beta-Yb5Sb3 reversible arrow Y5Bi3 types) for the former Er5Sb3 and Tm5Sb3 around 1100 degrees C and the means of quenching the high temperature Y form, have been esstablished. According to their magnetic susceptibilities, YB-types of Er5Sb3 and Tm5Sb3 contain trivalent cations. Tight-binding linear muff in-tin-orbital method within the atomic sphere approximation (TB-LMTO-ASA) calculations for the two structures of Tm5Sb3 reveal generally similar electronic structures but with subtle Tm-Tm differences supporting their relative stabilities. The ambient temperature YB-Tm5Sb3 shows a deep pseudogap at E-F, approaching that of a closed shell electronic state. Short R-R bonds (3.25-3.29 angstrom) contribute markedly to the structural stabilities of both types. The Y-type structure of Tm5Sb3 shows both close structural parallels to, and bonding contrasts with, the nominally isotypic, stuffed Ca5Bi3D and its analogues. Some contradictions in the literature are discussed.