Extreme pain 5 weeks after oral surgery, bone sticking out. Pain! Please help. Is this normal? (Photo)

You should be seen by your oral surgeon to re evaluate the area.  A small procedure may be needed to open the area and remove bony spicules and irrigate the area.  Good luck

Your oral surgeon is correct that this likely a small fragment working its way out. It may be a tooth/root fragment, bone fragment, dental filling fragment or it may be the sharp edge of attached bone around the socket that is projecting now that your body is remodeling the bone that was left after your surgery. Regardless of which one of these things it is, it can be removed (if it is not attached) or filed down/snipped off (if it is attached). Your surgeon should be able and willing to do this. It is a very common and painful post operative event. If left unresolved and protruding it can lead to an acute infection that can be difficult to resolve due to the location; it can also cause a raw ulcer to develop on the side of your tongue where it rubs. This ulcer will add a whole new level to your pain scale as the sharp protrusion continues to rub accross it preventing it from healing.
I would return and ask if it can be removed or filed down.

Pain is never normal.  It is not unusual to have some pain after having teeth removed and even for bone to work its way out after surgery but if you are having pain 5 weeks after surgery it is not normal.  I would go back to the surgeon and let them know what is going on.  Good luck!