I did some research into this at the time of his death. Although it does seem a high number of hours for a non professional, it is over a long period of time. 5900 hours over 44 years is only 134 hours per year. Of that, there would be in the region of 500 UK engagements per year where he would often fly to and from in royal flight Andovers, Wessexs etc. In addition to that, numerous tours and overseas visits. A recent BBC documentary showed a page of his logbook from a royal tour of the South Pacific, during which he flew numerous sectors.
I'm interested in how crewing would work for the royal flight though. Would one crew member be rostered to fly and then simply thrown out of their seat for a bit?