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Interplay of electronic correlations and spin-orbit interactions in Ir⁴⁺ and Ir⁵⁺ oxides results in insulating J_eff = 1/2 and J_eff = 0 ground states, respectively. By now, this has been well understood theoretically and established experimentally. However, in compounds where the dimerisation of Ir⁴⁺ and Ir⁵⁺ ions is structurally more favourable, the microscopic understanding of the local electronic structure is lacking. For example, a direct overlap of the Ir d-orbitals within the dimers may lead to significant bonding-antibonding splittings, which diminishes the role of spin-orbit mixing, considerably modifying the local electronic picture. With Ba₅AlIr₂O₁₁ as an example, we show that the direct d-d hybridisation effects are relatively weak, while electronic correlations (configuration mixing) and spin-orbit coupling play a dominant role. Using a combination of ab initio many-body wave function quantum chemistry calculations and resonant inelastic X-ray scattering experiments, we elucidate the electronic structure of Ba₅AlIr₂O₁₁. Our investigation shows that the two Ir ions (Ir⁴⁺ and Ir⁵⁺) in Ir₂O₉ dimer units preserve their local J_eff ground states close to 1/2 and 0, respectively.