We report the discovery of gamma-ray emission from the Galactic globular cluster Terzan 5 using data taken with the Fermi Gamma-ray Space Telescope , from 2008 August 8 to 2010 January 1 . Terzan 5 is clearly detected in the 0.5–20 GeV band by Fermi at \sim 27 \sigma level . This makes Terzan 5 as the second gamma-ray emitting globular cluster seen by Fermi after 47 Tuc . The energy spectrum of Terzan 5 is best represented by an exponential cutoff power-law model , with a photon index of \sim 1.9 and a cutoff energy at \sim 3.8 GeV . By comparing to 47 Tuc , we suggest that the observed gamma-ray emission is associated with millisecond pulsars , and is either from the magnetospheres or inverse Compton scattering between the relativistic electrons/positrons in the pulsar winds and the background soft photons from the Galactic plane . Furthermore , it is suggestive that the distance to Terzan 5 is less than 10 kpc and > 10 GeV photons can be seen in the future .