We report on the structural and magnetic properties of Li_5+xFe_1-xCo_xO₄ (0≤x≤1).< The system assumes two distinct crystal structures at room temperature (α and β), and shows a transition in preference from α to β between x=0.18 and x=0.25. This tendency is supported by DFT-calculations. Upon heating, Li₅FeO₄ undergoes a reconstructive transition from α→β at ∼1060 K, while Li₆CoO₄ shows an order-disorder transition from β→ϵ at ∼885 K, where ϵ is a cubic cation-disordered antifluorite structure. Li_5.50Fe_0.50Co_0.50O₄ is stabilised towards the ordered β-phase until at least 1170 K. XANES-measurements confirm that the oxidation states of Fe and Co remain unchanged throughout the series with charge compensation from additional Li⁺ on increasing x. Magnetic measurements show onset of low-temperature antiferromagnetic ordering around 3 K to 12 K. The magnetic structure of Li₅FeO₄ is described on the basis of powder neutron diffraction at 1.5 K, while the magnetic structures of Li_5.50Fe_0.50Co_0.50O₄ and Li₆CoO₄ are found to be slightly incommensurate below the ordering temperature.