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A computational tool that combines human-like chemical understanding with ab initio methods guides the compositional choice of complex five-component metallic oxides, yielding two new complex crystal structures.The discovery of new materials is hampered by the lack of efficient approaches to the exploration of both the large number of possible elemental compositions for such materials, and of the candidate structures at each composition1. For example, the discovery of inorganic extended solid structures has relied on knowledge of crystal chemistry coupled with time-consuming materials synthesis with systematically varied elemental ratios2,3. Computational methods have been developed to guide synthesis by predicting structures at specific compositions4,5,6 and predicting compositions for known crystal structures7,8, with notable successes9,10. However, the challenge of finding qualitatively new, experimentally realizable compounds, with crystal structures where the unit cell and the atom positions within it differ from known structures, remains for compositionally complex systems. Many valuable properties arise from substitution into known crystal structures, but materials discovery using this approach alone risks both missing best-in-class performance and attempting design with incomplete knowledge8,11. Here we report the experimental discovery of two structure types by computational identification of the region of a complex inorganic phase field that contains them. This is achieved by computing probe structures that capture the chemical and structural diversity of the system and whose energies can be ranked against combinations of currently known materials. Subsequent experimental exploration of the lowest-energy regions of the computed phase diagram affords two materials with previously unreported crystal structures featuring unusual structural motifs. This approach will accelerate the systematic discovery of new materials in complex compositional spaces by efficiently guiding synthesis and enhancing the predictive power of the computational tools through expansion of the knowledge base underpinning them.