Time-of-flight neutron diffraction measurements were carried out at 350 °C and 450 ± 5 °C for molten Bi5(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 D3h-Bi53+ structure:  d(Bia-Bie) = 3.2 Å and d(Bie-Bie) = 3.4 Å. The functions RDFrem(r) were simulated successfully by a model of intermediate range order similar to the environment in Bi5(AlCl4)3 crystals. The first sharp diffraction peak (FSDP) occurs at ca. 1.2 Å-1 and suggests a distance between Bi53+ and AlCl4- ions of about 5.5 Å in close agreement with values for the solid (5.6-6.2 Å). The free D3h-Bi53+ 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 QCISD(T)/LANL1DZ+PP level, distances of d(Bia-Bie) = 3.073 Å and d(Bie-Bie) = 3.331 Å were determined. The Bia-Bie distances consistently are shorter by about Δ(Bi-Bi) = 0.26 Å in the free ion, by ca. 0.3 Å in Bi5(AlCl4)3 crystals, and by ca. 0.25 Å in the liquid. Natural population analysis shows a larger charge on Bia (+0.74) than on Bie (+0.51). Natural electron configuration analyses show intact 6s-type Bi lone pairs. The lowest-lying cluster MOs are a1' (radial), e'' (mixed), a2'' (∥), and e'(⊥), and they are illustrated via contour plots of partial electron density functions. The molecular graph of Bi53+ shows compelling evidence for strong bonding along all edges.