The first Einstein@Home analysis of the early LIGO S5 data set, where the instruments initially reached their design sensitivity, began on 15 June 2006. This search used 22 segments of 30 hours each from the LIGO Hanford 4-km detector and six segments of 30 hours from the LIGO Livingston 4-km detector. This analysis run (code name "S5R1"), employing the search methodology as Einstein@Home, was very similar to the previous S4 analysis. However, the search results were more sensitive due to the use of more data of better quality compared to S4. Over large parts of the search parameter space, these results, which also appeared in Physical Review D, are the most exhaustive published to date.