They dont want their premiums to go up and they want me to pay?

Happened at a traffice light. She sped up and then slammed on her breakes and then I didn't really have enough time to do a complete stop. Rear ended her car. Total damages are nearly $6,000.00 My insurance wont cover them. The other party want me to pay out of the pocket this 6 grand instead of going through their insurance. Theres no police report. Of course I dont have 6 grand to throw around but if they just went through their insurance... What do I do?