We report the discovery of HAT-P-25b , a transiting extrasolar planet orbiting the V=13.19 G5 dwarf star GSC 1788-01237 , with a period P = 3.652836 \pm 0.000019 d , transit epoch T _ { c } = 2455176.85173 \pm 0.00047 ( BJD Barycentric Julian dates throughout the paper are calculated from Coordinated Universal Time ( UTC ) ) , and transit duration 0.1174 \pm 0.0017 d. The host star has a mass of 1.01 \pm 0.03 M _ { \sun } , radius of 0.96 _ { -0.04 } ^ { +0.05 } R _ { \sun } , effective temperature 5500 \pm 80 K , and metallicity [ Fe / H ] = +0.31 \pm 0.08 . The planetary companion has a mass of 0.567 \pm 0.022 M _ { J } , and radius of 1.190 _ { -0.056 } ^ { +0.081 } R _ { J } yielding a mean density of 0.42 \pm 0.07 g cm ^ { -3 } . Comparing these observations with recent theoretical models , we find that HAT-P-25b is consistent with a hydrogen-helium dominated gas giant planet with negligible core mass and age 3.2 \pm 2.3 Gyr . The properties of HAT-P-25b support several previously observed correlations for planets in the mass range 0.4 < M < 0.7 M _ { J } , including those of core mass vs. metallicity , planet radius vs. equilibrium temperature , and orbital period vs. planet mass . We also note that HAT-P-25b orbits the faintest star found by HATNet to have a transiting planet to date , and is one of only a very few number of planets discovered from the ground orbiting a star fainter than V= 13.0 .