The formation possibility of (Hf0.2Zr0.2Ta0.2Nb0.2Ti0.2)C high-entropy ceramic (HHC-1) was first analyzed by the first-principles calculations, and then, it was successfully fabricated by hot-pressing sintering technique at 2073K under a pressure of 30MPa. The first-principles calculation results showed that the mixing enthalpy and mixing entropy of HHC-1 were -0.869 +/- 0.290 kJ/mol and 0.805R, respectively. The experimental results showed that the as-prepared HHC-1 not only had an interesting single rock-salt crystal structure of metal carbides but also possessed high compositional uniformity from nanoscale to microscale. By taking advantage of these unique features, it exhibited extremely high nanohardness of 40.6 +/- 0.6GPa and elastic modulus in the range from 514 +/- 10 to 522 +/- 10GPa and relatively high electrical resistivity of 91 +/- 1.3cm, which could be due to the presence of solid solution effects.