The due date is the anniversary date (the 18th), or the first of the month, depending on what your agreement is with the landlord.
Most people expect to have a grace period to cover honest oversights, bank glitches, etc. And it's expected that you're not going to rely on this grace period every month, or at least that it'll be out of your hands, e.g. Your rent check is mailed and has a postmark of the 1st/18th every month, then postal transit time is not held against you.
This lease formally establishes the grace period, and defines it as 5 business days. It is not giving you an extra 5 days before the grace period begins. It is the grace period.
The adult response is to make every fair effort that the rent is paid on time, e.g. 18th or 1st.
If you push the limits of the grace period every month, the landlord has every right to judge you for that, and act accordingly. He can tell your references that you're a slow pay. He can decide he doesn't want to do you any other favors. He can tell you to move out (consistent with lease and law).