The pressure-induced transformation of diatomic nitrogen into nonmolecular polymeric phases may produce potentially useful high-energy-density materials. We combine first-principles calculations with structure searching to predict a new class of nitrogen-rich boron nitrides with a stoichiometry of B(3)N(5) that are stable or metastable relative to solid N(2) and h-BN at ambient pressure. The most stable phase at ambient pressure has a layered structure (h-B(3)N(5)) containing hexagonal B(3)N(3) layers sandwiched with intercalated freely rotating N(2) molecules. At 15 GPa, a three-dimensional C222(1) structure with single N-N bonds becomes the most stable. This pressure is much lower than that required for triple-to-single bond transformation in pure solid nitrogen (110 GPa). More importantly, C222(1)-B(3)N(5) is metastable, and can be recovered under ambient conditions. Its energy density of ∼3.44 kJ/g makes it a potential high-energy-density material. In addition, stress-strain calculations estimate a Vicker's hardness of ∼44 GPa. Structure searching reveals a new clathrate sodalitelike BN structure that is metastable under ambient conditions.