You need to review your written agreement to see whether there is a provision allowing the landlord to change due dates and amounts of late fees with proper notice to you. Usually, the notice period is 30 days.
Even if the landlord cannot change the terms, your "current lease is in effect until Oct. 31, 2013", meaning that it is about to expire anyway. If the landlord cannot change the current lease, you can expect that the new terms will be in the newer leases.
Either way, you should plan to pay the bills before they are due to avoid being charged late fees.
Presumably, the landlord can time when to issue the utility bill so that "20 days from when utility bill is issued" and "5th of the month" is the same day.