Interpretation of lease wording

[S. Perry]

My lease states that rent is due on or before the 1st day of each month. "Weekends, holidays, and mail delays do not excuse Tenant's obligation to timely pay rent."

It discusses the method of payment (direct deposit into a specified account).

This is what I have a question about how to interpret regarding late fees:

"If Landlord does not actually receive a rent payment in the full amount at the designated place of payment by 12:00pm on the 5th day of the month in which it is due, Tenant will pay Landlord for each late payment an initial late charge of $50.00 and an additional late charge of $10 per day thereafter until rent and late charges are paid in full (not to exceed 30 days)."

I had always read this to believe that I HAD to honor this type of grace period (for lack of a better term). My leasing agent said originally that he gives this 5 day period for emergencies (they can happen) but hopefully the tenant would not abuse it (they always have). When I keep reading this part of the lease I *think* in reality (correct me if I am wrong)....that I don't HAVE to accept rent late past the 1st if I don't want to but I just don't charge/collect a late fee prior to the 5th.

I can REFUSE rent if I so chose? My tenant deposits rent into an account that is only for their rent. I am half tempted to close the account so they can't pay rent for Feb. I am on the fence if I want them out or not due to too many lease violations to count. Waiting to hear from my attorney about a few issues but thought I would get opinions here from seasoned pros.