Thinner side armour?

I have wondered just how thin side armour can be and still provide some degree of protection to a large, fast warship. There would be some obvious advantage, if you would be able to accept 5in side armour, especially if the belt is 16ft high, at least. I would not want to have thinner armour than that, even if the upper belt. I am seriously thinking of taking my last design and doing just that, to see if there might be enough capacity to allow for greater speed.