Lease wording question about due/late date

[Michael Patterson]

My lease currently reads 

"Tenant agrees to pay the rent in advance of the first day of each month to ME to be deposited in our local Bank Account#00000000 or at such other place as management may designate. By paying the rent on time the Tenant will receive a discount of $_50_. In the event the rent is not received by the fifth of the month the discount is no longer applied."

I have a tenant that is paying on the 4th usually, which is no issue. Today is the fourth and no deposit. When I text-ed them to ask about it they said it would be in tomorrow the 5th. How do you interpret the wording above? 

A. The rent is due by COB on the 4th. The rent is late ON the 5th.

B. The rent is not late if received ON the 5th, but is late on the 6th.

This is the first time they have paid on the 5th, but have only been in the house 4 months. I don't plan on charging the $50 this time either way, but wonder whether I should bring it up as a reminder. In future leases I am going to reword that statement to be more clear.