The "first" 5th KY Inf was the mountain unit, that was later reorganized / newly organized in the fall of 1862. Some of these original men went into the reorganized (or newly organized) 5th Ky Inf (Col. Hiram Hawkins' regiment).
This 5th Ky Inf under Col. Hiram Hawkins joined the Orphan Brigade in the fall of 1863, and converted to mounted infantry in the fall of 1864.
The "other" 5th Ky Inf (Col. Thomas Hunt's regiment, in the Orphan Brigade from the beginning, later under Col. John Caldwell), that became the 9th Ky Inf, also converted to mounted infantry in the fall of 1864.
Geoff