Yes, when the original 12-month regiment (5th Ky. Inf.) was disbanded, there were two other units that were formed from this. One was a very short-lived reorganized 5th Ky. Inf. This regiment never existed except on paper, but there are muster rolls for the companies. Immediately following, this unit was disbanded and a "new" 5th Ky. Inf. was formed. This regiment served the remainder of the war, eventually being assigned to the Kentucky "Orphan" Brigade.
Many of the men in the original 12-month unit went into the new unit, but many went elsewhere (other KY units, other CS units, just went home, &c.). It can often be somewhat difficult to figure out where these other men went, without evidence from pension files, family history, &c.
Perhaps someone who has done a lot of research on the 5th Ky. Inf. units will jump in here with more info.
Geoff Walden