As I programmed it, you should be able to reach Librarian level 5, but the XP needed might need some balancing.
I'll try to add tracking in the form of a percentage number next to the level in the "My Progress" screen!
The librarian level requires intelligence, to reach librarian level 3 you need at least 2 intelligence levels that.
(As a correction, this means that level 5 is not obtainable yet but level 4 should be possible, I will nevertheless reduce the xp needed and increase the gain as it's too slow right now)
Edit: You were right, due to an error in the code the job couldn't be leveled up after level 2, I fixed it now and It will work correctly in the next update, thank you for reporting it!