Sir William Herschel observed the Sun from 1779 to 1818 with most of these solar observations made from 1799 to 1806. Wolf in reconstructing the long-term history of solar activity did not have Herschel's notebooks for analysis and thus was limited to scattered observations for the period 1801-1807. According to Wolf, the Wolf sunspot numbers for these years are very uncertain. Thus, by analyzing Herschel's notebooks, a better reconstruction of solar activity during cycle 5 is feasible. From Herschel's observations we find that the peak sunspot number occurred in 1801-1803 time period rather than 1805 as Wolf deduced. Instead of a solar cycle of 17 yr in length, we find a cycle length of 14 yr. Second, we find that the peak yearly mean sunspot number is only about 38 rather than 45 as Wolf deduced. Thus, this solar cycle was the weakest cycle since the Maunder Minimum and has been called the Dalton or Modern Minimum. Be-10, C-14, aurora records, and magnetic declination observations all tend to support these conclusions. In the course of this study, a technique for making early solar observations homogeneous with modern sunspot observations is developed and discussed.