Had a tooth extracted about 5 months ago, now seeing piece of tooth coming down thru gum line. what to do?

Tooth fragment: Most likely a piece of tooth fragment that has drifted to the surface. Could also be a sequestrum (bone fragment). Contact the dentist who extracted the tooth and request it be evaluated. Usually a very quick and easy procedure to remove, often without even anesthesia and part of the follow up care responsibility of the dentist.

Piece of tooth: In all probability it's not tooth, it's a small spicule of bone. Call the Dentist or Oral Surgeon who removed the tooth for a post-surgical reevaluation. The "fix" is easy.

Probably fine...: This is probably no big deal. Have your dentist take a look to give you a quick answer. If it hurts, bleeds, or swells up make the appointment asap.