Can this person legally sue me?

Last year in June, my brakes went out in my car at a redlight and my car hit the car in front of me. My car had already slowed down before the impact and I pulled my emergency break up when I realized my breaks weren’t working. The lady I hit jumped out of the car and claimed that her head hit the windshield and promptly called the police, even though it did not.

When the police officer arrived and listened to both sides of our story, he checked the breaks in my car and said that it was a no fault accident. The police report said there was no damage to either vehicle. When asked if she needed an ambulance, she declined.

Just a few days ago, I received a letter in the mail from the lady’s lawyer claiming that I owed her $5,000.00. The letter does not claim what for but asks for prompt payment in the form of a check. It also says I have 30 days to pay it or I will be sued in court. There is a number attatched and I have called it and left messages but no one will return my call.

Does this lady have a claim?