Melilite-type gallates of general formula RE1+xAE1-xGa3O7+x/2 are of interest for their ability to host mobile interstitial oxide ions in [Ga3O7+x] layers. The crystal structure of Ca5Ga6O14 is closely related to melilite, with [Ga3O7] layers stacked in a more complex way to accommodate an additional 0.5 interlayer cations per formula unit, suggesting the potential for similar oxide ion conduction behavior. We used a computational approach to identify the most promising routes to interstitial oxide incorporation into Ca5Ga6O14, leading to an experimental investigation of the system Ca5-xLaxGa6O14+x/2. Single-phase materials were obtained in the range 0 ≤ x ≤ 0.25 by solid state reactions, producing an ∼40× increase in ionic conductivity at 800 °C. This limited compositional range presents a challenge for characterization of the charge-compensating defects. The La substituents were observed directly by X-ray diffraction and STEM-EDX, and a combination of different structural characterization techniques and DFT calculations indicated the presence of interstitial oxide ions indirectly, explaining the conductivity response. As higher carrier concentrations (x > 0.25) are apparently inaccessible in this system, we conclude that its potential as a useful oxide ion conductor is more limited than that of established melilite materials such as La1+xCa1-xGa3O7+x/2.