Hm... This isn't really 5 but...
Rurouni Kenshin - Tokyo & Kyoto arc, as well as Tsuiokuhen OVA, as well as (not really anime) the FULL Seisouhen arc inthe manga
(I refuse to accept the last arc of the TV series as part of the story, because it was, IMO, sucky fillers made because they didn't want to wait patiently for Watsuki to finish Seisouhen and wanted to milk out money... and then when they animated Seisouhen they left out all the interesting stuff like Rakuninmura. :<)
Chikyuu Shoujo Arjuna (I don't care if it's preachy. ;P)
Just about every single Ghibli movie!
Princess Tutu (While I was sick of watching the last parts of the first few eps as they were so sweet and predictable, later it got quite good - and all the good stuff is hidden, you need to think and then you realise, DAMN this has some good things... and who can't resist Tchaikovsky
)
Gunslinger Girl (So far... I dunno what it is, I just like it. The OP also >you)
Aaaah, I forgot the rest. :|
Last Exile was pretty nice...
Arr, I'll throw in FLCL as well. Crazy as hell, but that's the point. XP