I am making a 5 tier wedding cake (6", 8", 10", 12" and 14") and I would like to know what you guys use as a cake board with a cake this heavy. I normally use a cake drum, but I'm assuming that won't be sturdy enough for this cake.

You could use an 18" piece of plywood.  I think a drum would work just fine as long as you lift it from the bottom instead of from the sides.

AAre you going to transport it stacked? If so, it will be WAY heavy. I was surprised how heavy just a 14 inch tier of carrot cake was.

Wood, for sure.  Anything else would likely collapse while carrying it.