Time-of-flight neutron diffraction measurements were carried out at 350 degrees C and 450 +/- 5 degrees C for molten Bi-5(AlCl4)(3), Contributions from AlCl4- were estimated using molten LiAlCl4 data and yielded radial distribution functions RDFrem(r) that allowed for the determination of the D-3h-Bi-5(3+) structure: d(Bi-a-Bi-e) = 3.2 Angstrom and d(Bi-e-Bi-e) = 3.4 Angstrom. The functions RDFrem(r) were simulated successfully by a model of intermediate range order similar to the environment in Bi-5(AlCl4)(3) crystals. The first sharp diffraction peak (FSDP) occurs at ca. 1.2 Angstrom(-1) and suggests a distance between Bi-5(3+) and AlC4- ions of about 5.5 Angstrom in close agreement with values for the solid (5.6-6.2 Angstrom). The free D-3h-Bi-5(3+) ion was studied with RHF, MP2, and QCISD(T) methods. Effective core potentials were used in conjunction with polarized split-valence LANL1DZ basis sets. At the QCLSD(T)/LANL1DZ+PP level, distances of d(Bi-a-Bi-e) = 3.073 Angstrom and d(Bi-e-Bi-e) = 3.331 Angstrom were determined. The Bi-a-Bi-e distances consistently are shorter by about Delta(Bi-Bi) = 0.26 Angstrom in the free ion, by ca. 0.3 Angstrom in Bi-5(AlCl4)(3) crystals, and by ca. 0.2(5) Angstrom in the liquid. Natural population analysis shows a larger charge on Bi-a (+0.74) than on Bi-e (+0.51). Natural electron configuration analyses show intact 6s-type Bi lone pairs. The lowest-lying cluster MOs are a(l)' (radial), e '' (mixed), a(2) '' (parallel to), and e' (perpendicular to), and they are illustrated via contour plots of partial electron density functions, The .olecular graph of Bi-5(3+) shows compelling evidence for strong bonding along all edges.