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If the tenant is under a fixed term written lease contract and it specifically states that a late fee will be applied to each payment, then yes, you can impose such a fee as this is something that would have been subject to negotiation at the beginning of the tenancy. When the tenant agreed to enter into the lease, they agreed to all the terms in it.
FL law doesn't cover late fee payments, but I would opine that as long as it is reasonable, if the tenant challenged it in court, it would be upheld.
And if there were fees of damages due at the end of the tenancy, they can be deducted from the security deposit as long as they are detailed in any security deposit damage letter...
As an aside, in addition to being an attorney, I have also been a landlord for over 26 years...