By solid-state reaction in closed ampoules, almost phase pure Swedenborgite CaBa(Mn₂Fe₂)O₇ [P6₃mc, a = 6.4100(1) Å, c = 10.3752(2) Å] was obtained. Thermodynamic and melting behavior investigations suggest that this complex oxide melts incongruently and that the true composition contains a minor surplus of Fe as compared to Mn. However, in first approximation, the magnetic transition metal lattice (Mn₂Fe₂) can be described as a homogeneous S = 5/2 system and consists of kagome layers with an intermediate trigonal site. A long range antiferromagnetic ordering is observed at T_N = 205.5 K, as proven by magnetometry and specific heat measurements. The S = 5/2 (high-spin d⁵) on-site configuration is confirmed by ab initio quantum chemical calculations, which additionally indicate antiferromagnetic Heisenberg interactions with a ratio of 1.56 between the spin coupling constants of the two distinct d⁵–d⁵ links (in and out of the kagome plane). In light of recent numerical studies for the extended Swedenborgite spin lattice, this quantum chemical estimate for the J_out/J_in ratio in combination with magneto-electric coupling, as a consequence of the polar, non-centrosymmetric crystal structure, explain the experimentally found antiferromagnetic order.