The noble gases are the most inert group of the periodic table, but their reactivity increases with pressure. Diamond-anvil-cell experiments and ab initio modelling have been used to investigate a possible direct reaction between xenon and oxygen at high pressures. We have now synthesized two oxides below 100 GPa (Xe2O5 under oxygen-rich conditions, and Xe3O2 under oxygen-poor conditions), which shows that xenon is more reactive under pressure than predicted previously. Xe2O5 was observed using X-ray diffraction methods, its structure identified through ab initio random structure searching and confirmed using X-ray absorption and Raman spectroscopies. The experiments confirm the recent prediction of Xe3O2 as a stable xenon oxide under high pressure. Xenon atoms adopt mixed oxidation states of 0 and +4 in Xe3O2 and +4 and +6 in Xe2O5. Xe3O2 and Xe2O5 form extended networks that incorporate oxygen-sharing XeO4 squares, and Xe2O5 additionally incorporates oxygen-sharing XeO5 pyramids. Other xenon oxides (XeO2, XeO3) are expected to form at higher pressures.