I didn't mention it, but if you click on the thumbnail at the top of the object sheet you can get a fuller image which expands even further. You can see the hand stitching.
As the sheet notes, this was the first battle flag to be captured in Virginia. It was part of the first silk issue and the center star is not missing. Twelve was the number for the first issues.
The state of North Carolina has produced a very comprehensive set of books called "North Carolina Troops 1861-1865, A Roster." If my memory serves me correctly, the first two are cavalry, the third volume is artillery and the fourth volume begins the infantry. I'd suspect the 5th Regiment would be included in this volume. The brief biographies of each soldier include the name, rank, dates of service, hospitalization, and circumstances surrounding his death if service-connected. This set of volumes can be found in just about any good sized municipal library in North Carolina. Some reseach libraries in Virginia surely have the Service Records on microfilm.
In fact some good-hearted researcher may be reading this right now who already has the information.
I'm an expatriot Tarheel now living in western South Carolina, so I don't really have ready access to the files, but I sure do wish you luck. You're very close.