The structure and mechanical response of grain boundaries (GBs) are essential for predicting the mechanical properties of polycrystalline materials. Understanding the properties of GBs in carbide ceramics is essential for the development of applications of high entropy carbide ceramics (HECCs) in extreme environments. In this work, we investigated the intrinsic properties and mechanical responses of {210}/[001] GBs in (HfNbTaTiZr)C HECC subjected to shear deformation and its constituent binary carbides using first-principles calculations. The results showed that the GBs in Group VB carbides undergo migration, whereas the formation of CC bonds within the GBs in Group IVB carbides can inhibit GB migration and result in the failure of supercells due to the breakage of metal-C bonds. Therefore, tailoring the GBs in (HfNbTaTiZr)C based on metal atoms from different groups can induce a "pinning" effect, potentially enhancing plasticity without sacrificing strength. Furthermore, HECC exhibits higher GB migration stress compared to conventional binary carbides. These results can provide in-depth insights into the mechanical behavior of GB structure of high-entropy carbide ceramics.