Four new compounds La5Re3MgO16 La5Re3FeO16 La5Re3CoO16 La5Re3NiO16 have been prepared by solid-state reaction and characterized by X-ray and neutron powder diffraction and SQUID magnetometry. Rietveld refinement revealed that the four compounds are isostructural with La5Re3MnO16 and crystallize in space group C1̄ with cell parameters a=7.9370(3), 7.9553(5), 7.9694(7), and 7.9383(4)Å; b=7.9998(3), 7.9960(6), 8.0071(8), and 7.9983(5)Å; c=10.1729(4), 10.1895(7), 10.182(1), and 10.1732(6)Å; α=90.190(3)°, 90.270(3)°, 90.248(4) °, 90.287(3)°; β=94.886(2)°, 95.082(3)°, 94.980(4)°, 94.864(3)°; γ=89.971(4)°, 90.001(5)°, 89.983(6)°, 89.968(4)° for Mg, Fe, Co, and Ni, respectively. The structures are related to a layered perovskite. The layers of corner-sharing octahedra Re5+M2+O6 (M2+=Mg, Fe, Co, Ni) are pillared by diamagnetic edge-sharing octahedra dimers, Re2O10, involving a Re=Re double bond. Three crystallographically independent lanthanum atoms occupy the three-dimensional interstices. All compounds obey the Curie–Weiss law at sufficiently high temperatures with Curie constants or effective magnetic moments near the expected values for the combination of Re5+(S=1) and M2+(S=0, 2, 3/2, 1 for Mg, Fe, Co, and Ni, respectively). Weiss constants, θC, are negative (−575, −84, −71, and −217K for Mg, Fe, Co, and Ni, respectively) indicating the predominance of antiferromagnetic exchange coupling. The phases for M=Fe, Co and Ni show long-range order at 155, 33, 36 and 14K, respectively. Neutron diffraction discloses a magnetic structure for the Fe series member consisting of ferrimagnetic perovskite layers coupled antiparallel along the stacking c-axis, direction which is consistent with the magnetic structure found recently for La5Re3MnO16.