I will play...
So I counted 8 faces before Hartnell, so Tom Baker would have been #12 and then Davidson #13, that scenario fits in with #5's regeneration. "Might Regenerate, I don't know..feels different this time." So he thought it should be the end of his life and did not know if he would regenerate. Perhaps he got an extended life span somewhere along the line and did not really know LOL Also explains some of instabilty of 6 being the first of a new life cycle.
Trouble is, in Mawdryn Undead Five made it plain he had regenerations left because he was considering giving them all up.
Yes, that and the Five Doctors at the time really cemented in that 5 was really 5. Still fun to flirt with the idea though lol