The crystal structures and the enthalpy-pressure phase diagram of P(3)N(5) were investigated by using density functional methods. Applying both approximations to the electron exchange and correlation gives a consistent picture for the two known polymorphs, alpha-P(3)N(5) and gamma-P(3)N(5). The calculated zone-center phonon modes compare very well with the experimental results. They indicate low-frequency bending modes for two-coordinate N atoms of alpha-P(3)N(5), which are responsible for a C2/c --> C c structural modulation of alpha-P(3)N(5) at moderate pressures. alpha-P(3)N(5) transforms into gamma-P(3)N(5) at pressures of about 6 GPa. We propose gamma-P(3)N(5) transforms into a delta-P(3)N(5) with Kyanite-type structure at pressures exceeding 43 GPa. Upon quenching, this triclinic modification of P(3)N(5) is likely to distort into a more symmetric monoclinic structure.