I would suggest starting with the Official Records and referencing any citation which mentions the regiment or its brigade. You might also ask a reference librarian at the Georgia State Archives what resources are available there. It may be that certain unpublished manuscripts or published sources can be copied for you.
Also, if you can learn the counties in which individual companies were raised, you may find county histories or local accounts which have chapters on the country's participation in the war. These may well describe officers and men of each company in some detail.
The 5th Georgia Regiment probably included several companies organized immediately after John Brown's raid on Harper's Ferry VA. For that reason, don't assume that the history of these companies started in the Spring of 1861 -- look at antebellum sources, such as newspapers and articles.