There was a John Rose, Co. G, 5th Arkansas Infantry, listed on a roll of men surrendered and paroled at Vicksburg, Mississippi, on July 8, 1863, but there are some problems with this. There is no John Rose carried on the rolls of that company, and the 5th Arkansas was not engaged at Vicksburg. I suspect the entry is an error.
Have you checked out the John Rose of Co. G, 14th (Powers') Arkansas Infantry? This regiment was recruited primarily in Marion, Searcy, Izard, Carroll, Newton and Fulton counties. This man was born c1832 in Tennessee.