In this work, a novel (Hf0.2Zr0.2Ta0.2Nb0.2Ti0.2)(N0.5C0.5) high-entropy nitride-carbide (HENC-1) with multi-cationic and -anionic sublattice structure was reported and their thermophysical and mechanical properties were studied for the first time. The results of the first-principles calculations showed that HENC-1 had the highest mixing entropy of 1.151R, which resulted in the lowest Gibbs free energy above 600 K among HENC-1, (Hf0.2Zr0.2Ta0.2Nb0.2Ti0.2)N high-entropy nitrides (HEN-1), and (Hf0.2Zr0.2Ta0.2Nb0.2Ti0.2)C high-entropy carbides (HEC-1). In this case, HENC-1 samples were successfully fabricated by hot-pressing sintering technique at the lowest temperature (1773 K) among HENC-1, HEN-1 and HEC-1 samples. The as-fabricated HENC-1 samples showed a single rock-salt structure of metal nitride-carbides and high compositional uniformity. Meanwhile, they exhibited high microhardness of 19.5 +/- 0.3 GPa at an applied load of 9.8 N and nanohardness of 33.4 +/- 0.5 GPa and simultaneously possessed a high bulk modulus of 258 GPa, Young's modulus of 429 GPa, shear modulus of 176 GPa, and elastic modulus of 572 +/- 7 GPa. Their hardness and modulus are the highest among HENC-1, HEN-1 and HEC-1 samples, which could be attributed to the presence of mass disorder and lattice distortion from the multi-anionic sublattice structure and small grain in HENC-1 samples. In addition, the thermal conductivity of HENC-1 samples was significantly lower than the average value from the "rule of mixture" between HEC-1 and HEN-1 samples in the range of 300-800 K, which was due to the presence of lattice distortion from the multi-anionic sublattice structure in HENC-1 samples.