Hi Jack,
For the 5th, there did exist one such history:
Kandelsdorfer, Major, Geschichte des k. u. k. Feldjäger-Bataillons Nr. 5.. Jägerndorf 1897.
https://books.google.com/books?id=S58sAQAAIAAJ&pg=PA224
https://books.google.com/books?id=Z6gaAQAAMAAJ&pg=PA1460
However, I have not found it yet. I could not even find its title in WorldCat.