Everyone's top five Futurama episodes are the same. The absolute best list is a pure, objective, immovable object.
(I don't want to hear any "my favourite episode isn't on the list". And I don't have comments so I guess I'm unlikely to)
The interesting list is 6-10 because that's where opinion divides. So, in no particular order (because this is all arbitrary enough; got to draw a line somewhere): 6-10 (OK; 6-11)
I'm not putting synopses with these because spoilers suck. If you want to read about the episodes, click the Wikipedia link and have at it.
And because I can never include the right number of things on a list.