I had a tooth extraction 5 days ago. The pain hasn't stopped and my gums are swelling regularly, usually every 3 hours. Please advise. I've had teeth extracted before and never had a problem.

Tooth extraction. This sounds like you have a dry socket or an infection, but it needs to be seen clinically and visually to make an accurate diagnosis. Call your dentist or surgeon ASAP for an examination.
Dry socket. I agree that you do have a problem now. You may have what is called Dry Socket. Normally after an extraction a blood clots in the empty space in your jaw and gradually heals in. Sometimes the clot doesn't adhere in the socket and this exposes nerves in the socket which become very painful. SEE YOUR DENTIST. He or she will fill the socket with a medicated dressing or special paste. OTC analgesics.