Diamond D5 is a hyperdiamond structured as coalesced C 20 and C28 small fullerenes, in the ratio 2:1, and having up to 90 % pentagonal rings while the others being hexagonal. Design of several precursors, intermediates, and crystal networks was performed using our original software programs CVNet and Nano-Studio. Energetic data, calculated at DFT and DFTB levels of theory revealed a stability of these structures close to that of classical diamond. A lonsdaleite-like structure is also discussed. The topology of these networks is described in terms of the net parameters and the net characteristics in crystallographic terms.