After my car accident, the doctor said I have a c5-6 disk protrusion - what does that mean?

Do you mean C 5-C6. Call the doctors office go back and get a full explanation and a copy of the report. There is no cervical 56. Perhaps they meant cervical spine c5 and c6 area of neck that the cervical disc is protruing out of line. I hope you are not in pain.
Herniated disc. The c5-6 herniation that you describe may or may not have come from the accident. In general, a disc herniation, which refers to the extrusion of tissue between two vertebral bodies, happens slowly. The accident, if it led to sudden pain, may have been causative or may have worsened a pre-existing condition.