We present high-precision photometry of two transit events of the extrasolar planetary system WASP-5, obtained with the Danish 1.54-m telescope at European Southern Obseratory La Silla. In order to minimize both random and flat-fielding errors, we defocused the telescope so its point spread function approximated an annulus of diameter 40 pixel (16 arcsec). Data reduction was undertaken using standard aperture photometry plus an algorithm for optimally combining the ensemble of comparison stars. The resulting light curves have point-to-point scatters of 0.50 mmag for the first transit and 0.59 mmag for the second. We construct detailed signal-to-noise ratio calculations for defocused photometry, and apply them to our observations. We model the light curves with the jktebop code and combine the results with tabulated predictions from theoretical stellar evolutionary models to derive the physical properties of the WASP-5 system. We find that the planet has a mass of Mb= 1.637 ± 0.075 ± 0.033 MJup, a radius of Rb= 1.171 ± 0.056 ± 0.012 R Jup, a large surface gravity of gb= 29.6 ± 2.8 m s−2 and a density of ρb= 1.02 ± 0.14 ± 0.01 ρJup (statistical and systematic uncertainties). The planet's high equilibrium temperature of Teq= 1732 ± 80 K makes it a good candidate for detecting secondary eclipses.