In this work, we report the detection of seven Neptune Trojans (NTs) in the Pan-STARRS 1 (PS1) survey. Five of these are new discoveries, consisting of four L4 Trojans and one L5 Trojan. Our orbital simulations show that the L5 Trojan stably librates for only several million years. This suggests that the L5 Trojan must be of recent capture origin. On the other hand, all four new L4 Trojans stably occupy the 1:1 resonance with Neptune for more than 1 Gyr. They can, therefore, be of primordial origin. Our survey simulation results show that the inclination width of the NT population should be between 7° and 27° at >95% confidence, and most likely ∼11°. In this paper, we describe the PS1 survey, the Outer Solar System pipeline, the confirming observations, and the orbital/physical properties of the new NTs.