The syntheses and distributions of binary R₅Pn₃ phases among the hexagonal Mn₅Si₃ (M), and the very similar orthorhombic β-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) Å, b = 9.176(1) Å, c = 11.662(1) Å), (b) the YB- and high temperature Y-types of Tm₅Sb₃ (both Pnma, a = 7.9262(5), 11.6034(5) Å, b = 9.1375(6), 9.1077(4) Å, c = 11.6013(7), 7.9841(4) Å, respectively), and (c) the YB structure of Lu₅Sb₃, a = 7.8847(4) Å, b = 9.0770(5) Å, c = 11.5055(6) Å. Reversible, temperature-driven phase transitions (β-Yb₅Sb₃ ⇆ Y₅Bi₃ types) for the former Er₅Sb₃ and Tm₅Sb₃ around 1100 °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 muffin-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 Å) 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.