You cannot go into f5 mode while on a moving donkey, however it does work when the donkey is still.

Put the summary of the bug you're having here

What I expected to happen was...:
For my player to go into third person (f5 mode) by pressing f5 while I was on a moving donkey

What actually happened was...:
Nothing changed

Steps to Reproduce:
1. get an a saddled donkey
2. hold "w" (Or your forwards key) and press f5