How long can a property manager claim damage, even after you paid the first claim?

Question Details: About 5 months ago, I moved out of my apartment after 9 years of residing at the complex. Around 2 weeks after I vacated the complex, they gave me a notice of repair for the apartment I moved from. Then a couple of weeks later when I was able to pay for the repairs that overextended the amount of my deposit, the apartment complex added new charges. I thought that was strange but made arrangements to pay anyway. After I had paid and received a notice saying that the account is closed and paid in full, 2 months later I received another notice claiming they found additional charges that they wanted me to pay for. Even after I told them I still have the invoice showing the account was closed and paid in full, and asked why are you coming at me 5 months after I had vacated the premises and 2 months after you told me that I was paid in full. I was told that they had up to 10 years to charge me for repair and my invoice means nothing. Is this true, and what will prevent them from coming up with additional charges in the future. I was also told if I don't pay within 15 days they will report me to the credit bureau that will show a negative on my report. Do I have any options legally to stop them from doing this to me and avoid continuously paying them for repairs that I assumed was taken care of?

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