No it shouldn't. The big 5 are Liverpool, United, Chelsea, Arsenal and now City, because they have won too much recently not to be. Teams like Tottenham and Leicaster have great teams, but they are not big clubs. They don't have the historical achievments the others have.
Tottenham and Leicaster can't become bigger than Arsenal or Milan for example, just because they have good squads for a few years and even win a trophy or two. The including of Tottenham in the super league was just because of their owner, not because they are a big club.