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From crystal chemistry rationale and density functional DFT calculations,novel tetragonal carbon C5 is proposed as simplest ultrahard allotrope withmixed hybrid carbon hybridizations (sp2 - sp3). Novel pentacarbon is identifiedas cohesive and stable both dynamically and mechanically. Whereas chargedensity is localized about tetrahedral C-sp3, it is found delocalized aroundtrigonal C-sp2 resulting in metallic behavior. The anisotropic structurecharacteristics caused by the aligned trigonal carbon along the tetragonalc-axis provide high Vickers hardness with a magnitude close to diamond

C5 as simplest ultrahard allotrope with mixed sp2/sp3 carbon hybridizations from first principles