Should I accept this settlement offer from the insurance company?

I got into a car accident on November 18 in Boston MA and the guy claimed to his insurance company that it was his fault so I'm not at fault. And because of this, I didn't call the cops or a police report or anything like that. He totalled my 2008 Honda Civic LX sedan 4D with 179,000 miles and it was worth $4,881 according to Kelly Blue Book, and the insurance company offered me $4,813.13. I had some back pain right after getting hit but that has since subsided. Lawyers have honestly been no help so far and this looks like a good offer but at the same time, I've heard that they don't really offer their best amount to start. They sent a check already but I haven't cashed it or anything.
Added (1). Actually, I do recall filing the Crash report a couple days later and did go to the police station but I didn't call them in the moment

Read more: Should I accept this settlement offer from the insurance company?