You actually carry a balance on your credit cards?
If you are paying interest on your credit cards, you are doing it wrong.
This is hardly anything new. You get a card with usurious interest rates for not paying completely on time if you want cashback/etc. benefits. You get a card with slightly less usurious interest rates and very limited benefits if you want to carry a a balance.
How do you have perfect credit if you're not paying your balances in full?
To maintain 'perfect' (which I doubt is 100% perfect) you just have to make your payments on time. It is okay to carry a balance. In fact, I remember my credit went up higher after paying off a balance I was carrying when I typically paid in full every month...
depends on how you use your credit card. You can get the 5% cash back and if pay everything in full on time you shouldn't even care about the interest rate.
Hell, 5% cash back even lets you break even for a couple months worth of interest if you are floating balances.