The electronic structure of the low-dimensional 4d5 oxides Sr2RhO4 and Ca3CoRhO6 is herein investigated by embedded cluster quantum chemistry calculations. A negative tetragonal-like t2g splitting is computed in Sr2RhO4 and a negative trigonal-like splitting is predicted for Ca3CoRhO6, in spite of having positive tetragonal distortions in the former material and cubic oxygen octahedra in the latter. Our findings bring to the foreground the role of longerrange crystalline anisotropy in generating noncubic potentials that compete with local distortions of the ligand cage, an issue not addressed in standard textbooks on crystal-field theory. We also show that sizable t2g 5−t2g 4eg 1 couplings via spin−orbit interactions produce in Sr2RhO4 ⟨Z⟩ = ⟨Σi li *si ⟩ ground-state expectation values significantly larger than 1, quite similar to theoretical and experimental data for 5d5 spin−orbit-driven oxides such as Sr2IrO4. On the other hand, in Ca3CoRhO6, the ⟨Z⟩ values are lower because of larger t2g−eg splittings. Future X-ray magnetic circular dichroism experiments on these 4d oxides will constitute a direct test for the ⟨Z⟩ values that we predict here, the importance of many-body t2g−eg couplings mediated by spin−orbit interactions, and the role of low-symmetry fields associated with the extended surroundings.