The syntheses and distributions of binary R(5)Pn(3) phases among the hexagonal Mn(5)Si(3) (M), and the very similar orthorhombic beta-Yb(5)Sb(3) (Y) and Y(5)Bi(3) (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 R(5)Pn(3) phases, R = Y, Gd-Ho, are generally confirmed. The reported M-type Er(5)Sb(3) 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 Er(5)Sb(3) (Pnma, a = 7.9646(9) A, b = 9.176(1) A, c = 11.662(1) A), (b) the YB- and high temperature Y-types of Tm(5)Sb(3) (both Pnma, a = 7.9262(5), 11.6034(5) A, b = 9.1375(6), 9.1077(4) A, c = 11.6013(7), 7.9841(4) A, respectively), and (c) the YB structure of Lu(5)Sb(3), a = 7.8847(4) A, b = 9.0770(5) A, c = 11.5055(6) A. Reversible, temperature-driven phase transitions (beta-Yb(5)Sb(3) left arrow over right arrow Y(5)Bi(3) types) for the former Er(5)Sb(3) and Tm(5)Sb(3) 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 Er(5)Sb(3) and Tm(5)Sb(3) contain trivalent cations. Tight-binding linear muffin-tin-orbital method within the atomic sphere approximation (TB-LMTO-ASA) calculations for the two structures of Tm(5)Sb(3) reveal generally similar electronic structures but with subtle Tm-Tm differences supporting their relative stabilities. The ambient temperature YB-Tm(5)Sb(3) shows a deep pseudogap at E(F), approaching that of a closed shell electronic state. Short R-R bonds (3.25-3.29 A) contribute markedly to the structural stabilities of both types. The Y-type structure of Tm(5)Sb(3) shows both close structural parallels to, and bonding contrasts with, the nominally isotypic, stuffed Ca(5)Bi(3)D and its analogues. Some contradictions in the literature are discussed.