What if the car accident is not directly your fault?
Actually, it doesn't matter. A car accident where your car insurance company not can recover the money from any other source or part. Will be classified as a fault accident even when the car accident is not directly your fault.
affect the next three to five years in your driving history.
If your car insurance company pay out if your car was stolen or involved in vandalism. Then you don't have to pay more on top of what you are already paying. The surprise comes when you want to renewal your insurance premium. So the car insurance premium will be higher and it will also affect the next three to five years in your driving history.
What if I change car insurance company because of the higher premium?
The new car insurance company will ask some questions about your car. They will ask you if your car have been involved in any car accident? Or other vandalism, events which you had make any claims? Remember to tell them the truth. The new car insurance company could easy find the information by ask your previous insurance company. Then they will find out about past claims. The insurance company then have a reason to invalidate your car insurance policy.