Hm, since you said that you enjoyed both Code Geass and Deathnote, I guess I can ease up on the "only recommending those 5 anime that I consider to be pretty much free of anime tropes" deal. Let's see... According to what you said you like, I'll just go ahead and put another vote in for Gurren Lagaan, because that shit is crazy and reaches absolutely maddening proportions relative to where it starts.
I'll also recommend Baccano, because Baccano is relatively free of anime tropes, and it is very unique and legitimately interesting to watch, and it is the only anime I know of that can easily shift between gruesome inhuman butchering of human bodies in horrific ways, to silly light-hearted comedy.
Those are the main things that come to mind at the moment, but I suppose now I can throw in some more personal recommendations. I'll be sure to edit my post if I think of something that fits your request.
I have to recommend One Piece, because it is my favorite anime, but the filler can get to be a bit much, like most other on-going shounen anime adaptation, but there are times when they go into filler arcs, which should be skipped, unless you like the filler. I highly recommend reading the manga, but since you don't want to read the manga, and this doesn't really quite fall within your preferences, I don't see that happening. One Piece does have an interesting cast of characters, atypical of the usual shounen cast, and it does break quite a few tropes. Oh, and despite the fact that it has been going for so long, there is actually a definite ending planned for the series, so it won't fall off into obscurity mid-way like many other series do when they realize that they have no idea how to continue the story.
I also have to recommend Hunter x Hunter 2011. For one, the new anime has a fairly large buffer so there's essentially no filler, and for two, I feel that Hunter x Hunter also breaks a lot of typical shounen tropes. It's very interesting seeing how the main character advances throughout the series, and it never has seemed like he was able to completely destroy a character that is obviously above his level purely by having a stronger will than the opponent. Oh, and also, plans actually work! In a lot of anime, plans don't seem to even matter, what with having strong wills and all, but I've noted multiple times where the main character(s) thought out a careful plan of action, that actually succeeded, or in the middle of a fight, the main character uses a secondary plan, which generally tend not to succeed in most anime, and actually manages to land a solid hit on a frighteningly strong opponent.
) and Soul Eater.
