If there is one thing I learned from all my car accidents, if it's not your fault go to the doctor immediately. And make sure you have a police report and call your insurance company immediately.
There are so many people that do not understand the amount of damage being rearended at only 5mph will do to your car. With today's car there is practically no such thing as a fender bender. My back bumper would cost at least $800 to replace, too many sensors, cracked or smashed it's the same outcome.
I will never deny an ambulance ever again. And never tell a doctor you are feeling better. It will bite you in the end.