Class 5 is a proprietary flush technology by Kohler, allowing to avoid clogging even if the toilet is meant to handle extraordinarily large masses of solid waste. The efficiency is achieved through a larger flush valve and direct jet fed.
As a result, a mass of water is let out in moments, flushing larger masses on its way. One of the tricks used for that involves making the entry of the flushing system is 1.5 times larger than the exit, thus forming extra pressure.
Let’s remember that cleaning the Augean stables with the power of two rivers was exactly the fifth labor of Hercules, though it’s merely a coincidence with the 5 in the name. Class 5 is a proprietary system, so it can only be found in Kohler toilets. American Standard, though, has something similar, named Double Vortex.