Given these foundational issues, it's folly to try to support Big Five or any other descriptive model just by saying that it's a good fit for the numbers. Any principal component analysis will find something which factors out as if it were a correlative component. This dooms Big Five just as reliably as it dooms g-factors or Myers-Briggs or any other astrology-like navel-gazing.
(If you want an example of actual five things showing up again and again and again, mathematics has examples [3][4][5], but it turns out that when actual five things show up, then the reaction is not to serenely admire the correlation, but to admit terror before cosmic uncertainty. Psychologists do not seem to go insane and kill themselves like statistical mechanics or set theorists; have they really seen the face of god?)
[0] https://en.wikipedia.org/wiki/Philosophical_zombie
[1] https://en.wikipedia.org/wiki/Dodo_bird_verdict
[2] https://en.wikipedia.org/wiki/Cartesian_theater
[3] https://en.wikipedia.org/wiki/ADE_classification
[4] https://en.wikipedia.org/wiki/Monstrous_moonshine
[5] https://en.wikipedia.org/wiki/Classification_of_finite_simpl...
[6] https://en.wikipedia.org/wiki/Hard_problem_of_consciousness