Pentazolate is the ultimate all-nitrogen, inorganic member of the azolate series of aromatic 5-membered ring anions. As an azolate ligand, it has the potential to form open framework structures with metal ions, that would be inorganic analogues of azolate metal-organic frameworks formed by its congeners. However, while the low stability and elusive nature of the pentazolate ion have so far prevented the synthesis of such frameworks, computational studies have focused on pentazolate exclusively as a ligand that would form discrete metallocene structures. Encouraged by the recent first isolation and structural characterization of pentazolate salts and metal complexes stable at ambient conditions, we now explore the role of pentazolate as a framework-forming ligand. We report a computational periodic density-functional theory evaluation of the energetics and topological preferences of putative metal pentazolate frameworks, which also revealed a topologically novel framework structure.