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Despite significant interest in their functional properties, the mechanical behavior of high-entropy oxides (HEOs) is not well studied, particularly at elevated temperatures. Bulk (Co,Cu,Mg,Ni,Zn)O (transition metal (TM)-HEO) samples were deformed under compression at applied stresses and temperatures ranging from 5 to 31 MPa and 600 to 850 °C, respectively. All of the deformation conditions result in creep stress exponents of n < 3, indicating that TM-HEO exhibits superplastic deformation. A transition from structural to solution-precipitation-based superplasticity is observed during deformation above 650 °C. Additionally, TM-HEO exhibits shear-thickening behavior when deformed at stresses above 9 MPa. The formation and behavior of a Cu-rich tenorite secondary phase during deformation is identified as a key factor underpinning the deformation mechanisms. The microstructure and phase state of TM-HEO before deformation also influenced the behavior, with finer grain sizes and increasing concentrations of Cu-rich tenorite, resulting in the increased prevalence of solution-precipitation deformation. While complex, the results of this study indicate that TM-HEO deforms through known superplastic deformation mechanisms. Superplasticity is a highly efficient manufacturing method and could prove to be a valuable strategy for forming HEO ceramics into complex geometries.