We present the discovery and timing solutions of five new pulsars by students involved in the Pulsar Search Collaboratory (PSC), a NSF-funded joint program between the National Radio Astronomy Observatory and West Virginia University designed to excite and engage high-school students in Science, Technology, Engineering, and Mathematics (STEM) and related fields. We encourage students to pursue STEM fields by apprenticing them within a professional scientific community doing cutting edge research, specifically by teaching them to search for pulsars. The students are analyzing 300 hours of drift-scan survey data taken with the Green Bank Telescope at 350 MHz. These data cover 2876 square degrees of the sky. Over the course of five years, more than 700 students have inspected diagnostic plots through a web-based graphical interface designed for this project. The five pulsars discovered in the data have spin periods ranging from 3.1 ms to 4.8 s. Among the new discoveries are - PSR J1926-1314, a long period, nulling pulsar; PSR J1821+0155, an isolated, partially recycled 33-ms pulsar; and PSR J1400-1438, a millisecond pulsar in a 9.5-day orbit whose companion is likely a white dwarf star.