I didn't see a doctor for five months after the accident. Now, the insurance company is saying there is a time limit to see a doctor and they won't pay me. Is this true? Is there a time limit to see a doctor?

There is no official time limit to see a doctor. What the insurance company is saying is that they do not believe that your doctor visit, five months after the accident, was caused by the accident. They are saying that you won't be able to convince a jury of that. So, while there is no official time limit, they are betting that you won't be able to prove the connection. Each case is different, but in the vast majority of car accident cases, waiting five months to see any doctor, and then trying to blame the car accident for that care, won't get you very far. The insurance company will probably win that battle.