My question is, is it feasible to 5 box 5 different classes?
I do 4, so I don't see why not. Mine is Pa/Pr/M/M/Wa. What it really comes down to is you have three "classes". Your main is your tank. Your healer. And your dps. Can you effectively use a warlock/mage/hunter and do decent dps close to each classes potential.

You are going to be playing a simplified version of each class, at least until you get a substantial amount of practice... and so what really matters is how simple and at the same time effective can you make them.

I was also tossing the idea around for 2 hunters and 2 warlocks, but can pets tank heroics?
Paladin/Warrior/Druid spec'd and geared is required for tanking heroics.