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One of the most promising applications of high entropy ceramics is their use as high temperature protective materials. Due to the additional entropic stabilization of the crystal structure, four- and five-element high entropy ceramics exhibit enhanced thermal and mechanical properties. For these applications, one of the most promising high entropy protective oxides are ZrO2- and HfO2-based protective HEOs. In this article, we study the HfO2–ZrO2–Y2O3–CeO2 equimolar system with the addition of MgO as a fifth component. We found that the HfZrCeY(Mg)O system maintains a single FCC crystalline structure up to the MgO concentration = 31.9 mol.%. Additionally, we determined that an addition of MgO at the close-to-equimolar HfZrCeY(Mg)O composition enhances the thermal properties of HEO, but reduces the mechanical properties such as hardness and resistance to crack formation. The minimum weight loss at the heating from RT up to 1450 °C was measured for the close-to-equimolar HfZrCeY(Mg)O composition at 18.4 mol.% MgO. The hardness of such composition was around 18 GPa. Due to the combination of these properties, the synthesized coating can be used as a protective material for high temperature applications, such as the protection of turbine parts.