Late fees on late fees? Consistently late rent

[Elizabeth V.]

Hello! I have an investment property in Athens, Georgia, where the tenant consistently pays rent late. In the lease there was a 5-day "grace period." Even with a generous grace period, although the tenant is current on rent, there are late fees from 3 months' rent on her balance. 

I am tired of her taking advantage of the grace period, so I am changing her lease to longer have this provision. Late fees will be charged the day after rent is due. For any new tenant I allow one grace period of five days per year. I've structured the late fee to be $25 on the first day, and $10 each additional day to encourage her to pay rent as soon as possible when it is late. 

I'm wondering if I could have a late fee on the late fees, such as $5 fee per day until ALL late fees have been paid in full. I want to discourage the tenant from not paying the fees. I haven't found any examples of late fees for late fees in other leases, but it does seem like in Georgia as long as it's in the lease, it's enforceable.

Does anyone have any thoughts or experiences they can share? Perhaps other strategies to get tenants to settle their late fees?