5000 miles is probably time to toss it anyway.

Is the pin hole the same distance from the valve stem?
If you had a tiny piece of wire protruding in the tire....and not removed-
Patch the tube, but flip its "orientation" and you have another pin hole. an equal distance from the valve.
Swab the inner tire with a cotton ball. IF there's a tiny wire, it'll tend to catch the cotton.