Here'sa quick easy run down.

Since I didn't give the required 15 days, how long does my landlord have to impose claim on my deposit?
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83.49 F.S. :
When you move out, the landlord must either return your deposit within 15 days of termination of the rental agreement, if the landlord does not intend to impose a claim upon the security deposit; or justify in writing by certified mail, to the tenant's last known mailing address within 30-days upon termination of a rental agreement, as to why they are keeping a portion of or all of the deposit. If the notice is not sent as required within the 30-day period, the landlord forfeits his/her right to impose a claim upon the deposit, unless you fail to give proper notice prior to vacating.
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Section 83.57, F.S.
Termination of tenancy without a specific term - days of written notice required (prior to termination):

Weekly --------- 7 days
Monthly -------- 15 days
Quarterly ------- 30 days
Yearly ---------- 60 days
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15 days is a pretty small window (most it's 30), so doesn't give much time to clean up/ re-rent. In all honesty, were it me and that was the law, if you were only off by 2 days (even if it was verbal), if the place was left in good condition and not a PIA for me, I'd let it slide. But there are some LL's out there who let nothing slide.

Are they easy people to deal with? Because at this point it certainly sounds like you could legally be out your SD based on the Notice law. But maybe they're willing to take the 13 days (even if it was verbal) and let it go at that.

However, if it looks like they're going to hold the SD on that count, nothing lost on your part if you nicely tell them you're sorry, didn't realize what was required of you being a first time renter. (Then if there are any positives such as always paid on time, left it clean, humbly toss those in as well.) I would encourage you not to even remotely come off with an attitude, especially of entitlement. Not saying you will, mind you. But I see it all the time and it backfires. Tho personally tend toward the lenient side myself, if someone has left me with issues and shows entitlement or aggression, they've lost any extra cooperation or flexibility from me.

At this point you've nothing to lose by contacting them to check the status.

According to Part 5 of statute 83.49 a 7 days' written notice by certified mail is required or personal delivery. If not given, that nulls the 30 days required by the landlord to send me a notice of intent to withhold funds. I did give them a 8 day notice by mail but it wasn't certified. I wonder if that includes back rent too?

My problem is now that I'm completely confused. If the rules don't apply, how long can a landlord wait before making a claim? Months, years?