This theory states that each incarnation channels what it was five changes back just as much or more than any other. For example, the Sixth Doctor channels as much or more of the First Doctor than he does the Fourth Doctor, the Seventh Doctor likely channels more of the Second Doctor than he does even the First Doctor, the Eighth Doctor channels as much of the Third Doctor as he does of the Fourth and Fifth Doctors, and the Tenth Doctor channels more of the Fifth Doctor than just about anybody else. Like anything else, roadblocks hit this theory that sundered the fanbase.

First of all, the Ninth Doctor seems to be somewhat removed from the Fourth Doctor, and the Eleventh Doctor is more like the Second and Fourth Doctors than he is the First and the Sixth, and then we have the War Doctor, who is definitely based around the First Doctor.

Luckily, I think I thought of a way to patch that up.

First of all, the Ninth Doctor is not wholly removed from the Fourth Doctor: The Fourth Doctor was not always silly, he had some sterner moments during the Philip Hinchcliffe era, and for God's sake, the Ninth Doctor wasn't always screaming with rage! That was mostly just in Dalek, which seems to be the only Ninth Doctor story anybody ever talks about, even though eight out of his ten stories were good.

...Still, saying that the Ninth isn't like the Fourth enough for the Take Five Theory to hold true is still fair on the grounds that the Ninth is not only as much like the First as he is the Fourth, but he's probably got even more of the Second Doctor than he does either the First or the Fourth (the hyperactivity and overall jittery nature of the Ninth Doctor was only matched by Troughton until other Revival Doctors popped up, and his bizarre, made-on-the-fly, and sometimes rather Machiavellian strategies, like the ones employed in Journey's End, were largely Troughtonesque).

So how to explain this? And what about the Eleventh Doctor?

We can actually thank Moffat for this.

The Grand Moff not only gave us the War Doctor, but also made the Tenth Doctor's second regeneration count, and few other writers would have come up with that. The War Doctor was an artificially induced regeneration, even more so than the Doctor's second regeneration because the Eighth Doctor wasn't even alive when it happened. It was completely and totally Karn, and thus the new regeneration was heavily altered in personality so that he would be a solid Warrior. This meant that he couldn't become mostly or equally Fourth Doctor as he would have been naturally. This meant that he had to change twice more in order to recover and go back to the Five-packs on their usual schedule. As the War Doctor mostly channeled the First Doctor, the incarnation that followed would largely channel the Second Doctor, but there was a lot of Fourth Doctor trying to come out during this time. When he turned into the Tenth Doctor, he was basically back to his usual five-pack schedule, albiet he had some Pertweean traits at first, but these were quickly supplanted after Rose Tyler was gone.

As for the Eleventh Doctor, because the Tenth essentially cheated himself of a regeneration, he also once again set back the five-packs, and when he finally turned into the Eleventh Doctor, he once again channeled the Second Doctor more than the rest.