I read a little more last night and found that the date of Sept. 12, 1862, corresponds with when Gen. Bragg and Kirby Smith moved their forces into Kentucky in their attempt to restore Kentucky to the Confederacy and to bring on new recruits. Bragg had ordered Humphrey Marshall to Salyersville and they arrived on 9/12/62. They must've been met there by a number of anticipatory recruits anxious for the return of a confederate presence in the area. It makes sense that Andrew and Henry were also there to greet them. You'll notice if you go through the 5th's roster, that a number of new recruits enlisted on or around Sept 12th.

When Bragg's army retreated following the Battle of Perryville in late October, this also corresponded with the end of the one year enlistments of many of those in the 5th. The others who had recently signed on for three years could very likely have not been too excited about leaving the area and their homes with the army and used that opportunity to 'desert'. Bragg later made some exasperated comments about the commitment level of the inhabitants of Kentucky and was very disappointed at the lackluster results of the overall recruiting campaign.