From the posts, in response to your query, I'm not sure if you're looking for the 5th NC Infantry or 5th NC Cavalry. It appears, however, that you're looking for the 5th NC Cavalry.
If that is the case, there is no formal published regimental history. Please see the next 'graf for a citation which I think is what you're looking for.
McRae, James C. "McRae's Battalion North Carolina Cavalry," sketch found in Walter Clark's Histories of the Various Regiments from North Carolina in the Great War, Vol. IV. pp. 379-382.