We report the discovery of TrES-5, a massive hot Jupiter that transits the star GSC 03949-00967 every 1.48 days. From spectroscopy of the star we estimate a stellar effective temperature of T-eff = 5171 +/- 36 K, and from high-precision B, R, and I photometry of the transit we constrain the ratio of the semimajor axis a and the stellar radius R-star to be a/R-star = 6.07 +/- 0.14. We compare these values to model stellar isochrones to obtain a stellar mass of M-star = 0.893 +/- 0.024 M-circle dot. Based on this estimate and the photometric time series, we constrain the stellar radius to be R-star = 0.866 +/- 0.013 R-circle dot and the planet radius to be R-p = 1.209 +/- 0.021 R-J. We model our radial-velocity data assuming a circular orbit and find a planetary mass of 1.778 +/- 0.063 M-J. Our radial-velocity observations rule out line-bisector variations that would indicate a specious detection resulting from a blend of an eclipsing binary system. TrES-5 orbits one of the faintest stars with transiting planets found to date from the ground and demonstrates that precise photometry and followup spectroscopy are possible, albeit challenging, even for such faint stars.