The 5800 and 5802 models were based on contracted design work done by Nelsen Pass. I have owned both. I liked the 5800 better sonically as it had a noticeably better bottom end in my system (deeper, more impact). I did not like the fan noise however. I think you would be happy with the 5802 and agree with other posters who say it's a big step up design-wise from the 555.
While these Adcoms are well built and an even better value at used prices, they getting older. Just a slight caution that it may not be that easy to get it repaired if something goes wrong as some parts are not readily available. I know this from personal experience.