What Are The NC Laws Concerning Eviction For Slow Pay (3 Days After 5 Day Grace Period)?

My landlord gave me a letter in the mail suggesting threat for the rent being past due. The letter was written and mailed on the back of a eviction info sheet from the local courthouse the day after the 5 day grace ended. According to the lease agreement the late pay is grounds for a breach of contract but then goes on to say that for late payment a $75.00 late charge will be added to the next months rent. So begs the question, is the lease broken or isn't it? And is there an allotted repayment time?