This paper presents results of an all-sky search for periodic gravitational waves in the frequency range [50,1 190]  Hz and with frequency derivative range of ∼[−20,1.1]×10−10  Hz s−1 for the fifth LIGO science run (S5). The search uses a noncoherent Hough-transform method to combine the information from coherent searches on time scales of about one day. Because these searches are very computationally intensive, they have been carried out with the Einstein@Home volunteer distributed computing project. Postprocessing identifies eight candidate signals; deeper follow-up studies rule them out. Hence, since no gravitational wave signals have been found, we report upper limits on the intrinsic gravitational wave strain amplitude h0. For example, in the 0.5 Hz-wide band at 152.5 Hz, we can exclude the presence of signals with h0 greater than 7.6×10−25 at a 90\% confidence level. This search is about a factor 3 more sensitive than the previous Einstein@Home search of early S5 LIGO data.