A 10-layer hexagonal perovskite Ba5Sb1−x
Mn4+x
O15−δ solid solution (0.24 ≤ x ≤ 0.36; space group P63/mmc, a = 5.7095(1) Å, and c = 23.4866(3) Å for x = 0.36) has been synthesized by solid state reaction and studied using powder X-ray and neutron diffraction and magnetization measurements. This 10H polytype structure contains one corner-sharing (Sb,Mn)O6 octahedron and a tetramer of four face-sharing MnO6 octahedra per formula unit. Two magnetic transitions are observed at 129−167 K (T
M) and 13−22 K (T
F). The frustration index |θ|/T
M, where θ is the Weiss temperature, is very close to unity, but considerable magnetic frustration is evidenced through the long-range order of a small ∼0.5 μB antiferromagnetic moment below T
M, and the formation of ferro- or ferrimagnetic clusters. These freeze at T
F with the |θ|/T
F ≈ 7−10 index representing high magnetic frustration. T
F increases directly with the excess of Mn, x, in Ba5Sb1−x
Mn4+x
O15−δ rather than with the overall Mn content, showing that the occupation of the corner-sharing Sb/Mn sites is key to the extended magnetism.