no way. the discus could fit in there, but just barely at adult size, and keeping the water clean enough could turn into a problem.
as for the angels, having that many would turn your tank into a war zone. IME, 4 of them in a 55g is a constant battle for territory, and even worse when they start pairing up and trying to breed. i upgraded my 4 angels from a suddenly cramped 55g to a 150g tank, and they still chase and fight even with plenty of room. i wouldn't go with more than 2-3 angels in a 55, but that leaves plenty of room for other fish (tetras, rasboras, loaches, cory cats, small plecos, etc...) and still allows you to have angelfish without the aggression problems of having too many packed together. of course, starting 6-8 (or more) young ones in a 55 is fine if, for example, you wanted to breed them. then you could remove pairs from the 55 as they form and set them up in individual breeding tanks. otherwise, there's no way they could all live together once they start to mature and not be stressed out and shredded up all the time.
Discus do not need a large volume of water to swim in imo as they are not very active fish at all. Also, they are not much bigger than angels at all. Lastly, water quality would be the issue. In my 72g, I must do water changes every two to three days(I have four). In a 55g that would probably be reduced to at least once a day due to the reduced volume of the tank.
I would buy them at around 4in in order to be able to feed them less(than 2in or so) and pollute the tank a lot less.
like everyone have known, i used to have 6 discus and 2 angels in a 20 long, but now i bought my new 55 gal(48x13x20) so i move them over, the angel have paired, but no agression at all, also 2 of my discus, they are living happy