Ancestry is a wonderful place for most types of information. For some reason, much of Ancestry's Civil War data misleads or confuses people. In any case, we get to clear up lots of confusion that be traced back to Ancestry.
People who are new to Civil War records usually assume that a name match with their ancestor confirms his service in a particular unit. In fact several different men sharing the same name can often be found in the same state. Evidently that's the case with Mathias Baynes.
Aside from name and age, the next information needed is a man's home county in 1860. Having done your homework, we know Mathias Baynes lived in Choctaw County. Since no company from the 5th Alabama Regiment came from Choctaw County, we must look elsewhere.
Your source placed Mathias Baynes in the 1st Alabama Regiment. He's probably Matt R. Bane, who belonged to Alpheus Baker’s 1st Alabama-Tennessee-Mississippi Regiment. The regiment included four companies from Alabama, four companies from Tennesse, and two from Mississipi. Bane's company, the "Andy Moore Guards", organized at Butler, Ala., Sept. 8, 1861. This company was accepted in state service four days later, and mustered in Confederate service at Camp Johnston near Memphis, Tenn., Oct. 15, 1861.
When the 1st Alabama-Tennessee-Mississippi Regiment organized at Fort Pillow, Tenn., Dec. 27, 1861, the "Andy Moore Guards" became Company "F". Assuming that officers and men of this command came from Memphis, the War Department recognized this regiment as the 39th Tennessee. Eventually the mistake was recognized and it was designated the 4th Confederate Regiment.
This man's service file with the 4th Confederate Regiment includes only prisoner-of-war records. These show that he surrendered with his command at Island Ten on April 8, 1862. He was taken to Camp Randall, Madison, Wisc., where several of his comrades died. They are buried just outside the football stadium for the University of Wisconsin. He was then sent to Camp Douglas in Chicago on June 9, 1862. Eventually he was placed on the steamer John H. Done and sent to Vicksburg for exchange. This took place on Sept. 20, 1862.
Here's some information on Camp Randall and Confederates imprisoned there --