Recently, Wei et al. proposed a superhard tet-C 5 allotrope with mixed carbon hybridization (sp 2 and sp 3 ) and metallic character based on structure prediction programs and first-principles calculations within DFT . However, such 'pentacarbon' should be unstable because it has some negative elastic constants. Later, in 2020, cubic 'pentadiamond' was reported as a novel allotrope with mechanical properties close to diamond, but the paper was retracted due to serious errors in the optimized structure of 'pentadiamond' under mechanical deformation admitted by the authors themselves . Such interest in С 5 allotropes with mixed carbon hybridization arises from the possible change of the electronic structure of insulating diamond, leading to metallic-atoms. The mechanical, dynamic and thermal properties are detailed in Sections 5, 7 and 8, respectively, and the electronic band structures are discussed in Section 9.