We report the discovery of WASP-5b, a Jupiter-mass planet orbiting a 12th-mag G-type star in the Southern hemisphere. The 1.6-d orbital period places WASP-5b in the class of very-hot Jupiters and leads to a predicted equilibrium temperature of 1750 K. WASP-5b is the densest of any known Jovian-mass planet, being a factor seven denser than TrES-4, which is subject to similar stellar insolation, and a factor three denser than WASP-4b, which has a similar orbital period. We present transit photometry and radial-velocity measurements of WASP-5 (= USNO-B1 0487-0799749), from which we derive the mass, radius and density of the planet: M_P = 1.58 +0.13 -0.08 M_J, R_P = 1.090 +0.094 -0.058 R_J and Rho_P = 1.22 +0.19 -0.24 Rho_J. The orbital period is P = 1.6284296 +0.0000048 -0.0000037 d and the mid-transit epoch is T_C (HJD) = 2454375.62466 +0.00026 -0.00025.
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