I think dropping one is a good idea just because you're not going to be made an offer based on 5. If your motivation were a fascination with the subjects, then... but the concern about socialising suggests it's largely grandstanding. You don't want to miss an offer because spreading yourself too thin.
Maths is the one that's non-negotiable. At a number of places Further Maths counts only as a fourth (or fifth, sixth...) A-level. For the LSE and perhaps for Cambridge it'll strengthen your hand.
I'd drop one of Physics or Economics. Probably Physics. History is going to be handier than you yet know, or will be at any of these other than the LSE.