In this work, high-entropy composite bulk ceramic of (Hf_0.2Zr_0.2Ti_0.2Nb_0.2Ta_0.2)N/silicon carbide (HEN–SiC) was fabricated via spark plasma sintering (SPS) at 2100 °C with submicron-sized single-phase (Hf_0.2Zr_0.2Ti_0.2Nb_0.2Ta_0.2)N (HEN) powder as a raw material and SiC particles as a sintering aid. The crystal structure, phase composition, and grain size/morphology of the composite were characterized by X-ray diffraction, scanning electron microscopy, transmission electron microscopy, and energy dispersive spectroscopy. The relative density and mechanical properties (i.e., bending strength, Vickers hardness, and fracture toughness) of the composite bulk ceramics were analyzed. The results show that the relative density of the composite bulk ceramics with increasing SiC particle content from 0 to 10.0 wt% increases from 93.08%±0.13% to 99.12%±0.12%. The high-entropy composite bulk ceramic with SiC particle content of 10.0 wt% exhibits the optimum mechanical properties (i.e., Vickers hardness of 23.34±0.67 GPa, fracture toughness of 4.35±0.13 MPa·m^1/2, and bending strength of 409±11 MPa) compared with the ceramic without SiC particles (i.e., Vickers hardness of 19.16±0.56 GPa, fracture toughness of 3.78±0.09 MPa·m^1/2, and bending strength of 335±11 MPa). These results indicate that SiC particles can be distributed and fill the HEN grain boundaries in the ceramic matrix, promoting composite densification via pinning grain boundaries and inhibiting grain growth. The enhanced fracture toughness can be due mainly to fine-grain toughening in addition to lamellar/chain structure toughening. The use of SiC as a sintering aid can promote the densification and fracture toughness of high-entropy nitride bulk ceramics, providing a promising approach for the preparation of high-density, high-performance high-entropy nitride bulk ceramics.