A new family of quaternary fluoro-antimonides A₅Cd₂Sb₅F (A = Sr, Ba, Eu) and oxyantimonides Ba₅Cd₂Sb₅O_x (0.5<x<0.7) have been synthesized and structurally characterized. The title compounds are isotypic, and crystallize with a novel structure type in the orthorhombic space group Cmcm (Z = 4, Pearson symbol oC52). The crystal structures feature one-dimensional double-strands of corner-shared CdSb₄ tetrahedra, [Cd₂Sb₅]⁹⁻. The arrangement of the chains is such that two of the unshared Sb vertices are close together to form a Sb–Sb bond, effectively making pentagonal quasi-channels. One of the five A²⁺ cations reside inside the tubes with the remaining four surrounding them. The electron balance is provided by O²⁻ or F⁻ anions, which fill suitable tetrahedral holes, left between the outer A²⁺ cations. The chemical bonding in the new family has been investigated using TB-LMTO-ASA band structure calculations, which suggest that the presence of the electron acceptor, oxygen or fluorine, is essential for optimization of the bonding interactions.