Many of the people who post here on A-gon have owned Adcom amps at one time or another. I've owned 5 different Adcom power amps since the late 1980's, including the 5500/5503, but I have not owned the 5802. I also sold Adcom products in the early 1990's (which was prior to the production of the 5802).
Personally speaking, I think that Adcom products offer good sound quality and very good value. The amps tend to have a "family" sound, mostly due to similar circuit design, the use of MOSFET transistors, and similar chassis construction techniques. The larger amps are on the somewhat warm side, but still fairly revealing with very good mid-range, decent imaging and transient response, and very good bass control. The one area of the frequency response where the Adcoms may tend to sound a bit "soft" (to my ear) is in the high frequencies (above 10kHz).
For many years, when their products were being made in Taiwan, Adcom had excellent parts and quality control. They still have high quality parts -- some are actually MIL-SPEC -- but there have been some QC issues during the past several years since they switched their manufacturing to China.
While I have not had direct experience with the 5802 amp, I have listened to one owned by a friend, and I think it is a very good amp. If you can buy a used one, it is also an excellent value. The only "negatives" I can offer about the 5802 are: size (it's quite tall), and heat output (it tends to run quite hot due to class-A biasing). Therefore, you need to be sure that you have adequate space and ventilation for this amp.
Hope this helps.