Aside from the numbered chapters introduced by Christianity, what is the source for dividing the Torah into parshot (weekly Torah reading) and the 5 volumes (Bereishit, Shemot, Vayikra, Bamidbar and Devarim)?
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There is scarce mention in the Talmud of specific Parshas as we know them. The only Parshiyos named are Tetzaveh, Ki Sisa, and Vayakhel (Megillah 29b-30a). Other than that, there is mention of certain sections of the Torah being read at certain times of the year (for example, the curses of Toras Kohanim before Shavuos - Megillah 31b), but no mention of any Parshas. There is an allusion to a standardized alloted amount of text, in the imperative to finish something called פרשיות together with the congregation, in the dictum of שנים מקרא ואחד תרגום (Berachos 8a), however no mention of anything weekly is explicitly discussed. The practice of weekly Torah reading is in the Talmud (e.g. Bava Kamma 82a), but the divisions of how much to read (other than bare minimums per aliyah) are not.
However, the Mogen Avrohom (O.C. 282 introductory remarks) cites the Zohar in Parshas Vayakhel Amud 369 as referring to Parsha divisions, in which the Zohar refers to not splitting the words from one Shabbos off to another Shabbos.
I heard a recording of Rabbi Y.S. Shorr (on Parshas Nasso), in which he referred to the Zohar as indicating that the Parsha separations predate the Anshei Knesses HaGedolah.
The siddur of R' Saadia Gaon (עמוד שסד) is the earliest source of which I am aware that lists the names of all the Parshiyos (although he leaves out Vayeilech).
References to the division of the 5 books can be found at least as early as the Mishnaic period. For example, the above quoted Gemara from Megillah 31b refers to two of the books by the names which Chazal gave them (Toras Kohanim for Vayikra and Mishneh Torah for Devarim).
For the sources used and to read more: http://www.biu.ac.il/js/JSIJ/8-2009/Stulberg.pdf