The structure of the Si(111)-(5×2)-Au surface, one of the long-standing problems in surface science, has been solved by means of Weissenberg reflection high-energy electron diffraction. The arrangement of the Au atoms and their positions with respect to the substrate were determined from a three-dimensional Patterson function with a lateral resolution of 0.3 Å based on a large amount of diffraction data. The new structural model consists of six Au atoms in a 5×2 unit, which agrees with the recently confirmed Au coverage of 0.6 ML [I. Barke et al., Phys. Rev. B 79, 155301 (2009).]. The model has a distinct ×2 periodicity, and includes a Au dimer. The model is also compatible with previously obtained STM images.