Had tooth extraction 5 years ago and area in gums/jaw still hurts. Anyone have this problem?

I should have answered this the first time I read it. I had a bridge put in over a decade ago and it always felt like I had a seed under it...was vigorously flossing with the fuzzy floss in that area every day. It finally worked loose and fell off, ended up having surgery a few years ago to have the teeth removed, there was a tiny bit of latex that had gotten embedded in that area that felt like a seed was embedded, had to go to a dental surgeon instead of a dentist and have surgery. The tiny bit of latex never showed up on dental x-rays either, the first dentist was going to extract the teeth and saw the blue material and sent me to a surgeon because she didn't know exactly what was going on.

It could be anything. I would suggest to change dentist and have them adjust your bite. Your jaw may be out of alignment. Or there could be an infection or the loss one one tooth may have made the other one sensitive. That happened to me before I had an implant to fill in the missing tooth.

Have they done a CT and MRI to rule out bone or soft tissue infection?

Perhaps they hit a nerve.

Maybe it's infected ?

Sounds like nerves

Ask your dentist.