It has been well established experimentally that the 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. However, in compounds where the structural dimerization of iridium ions is favorable, the direct Ir d-d hybridization can be significant and takes a key role. Here, we investigate the effects of direct Ir d-d hybridization in comparison with electronic correlations and spin-orbit coupling in Ba5AlIr2O11, a compound with Ir dimers. 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. We find excellent agreement between the calculated and the measured spin-orbit excitations. Contrary to expectations, the analysis of the many-body wave function shows that the two Ir (Ir4+ and Ir5+) ions in the Ir2O9 dimer unit in this compound preserve their local J(eff) character close to 1/2 and 0, respectively. The local point group symmetry at each of the Ir ions plays an important role, significantly limiting the direct d-d hybridization. Our results emphasize that minute details in the local crystal field environment can lead to dramatic differences in the electronic states in iridates and 5d oxides in general.