35 are the books of Tanach as they would appear in a scroll.
While we usually count 24 (counting the Twelve as one), Yoreh Deah 384283:1 specifies that when writing one giant Tanach scroll, the same multi-space break between books is also used between sub-books of the Twelve. So 35 blocks of text altogether.
(Poor Nechemiah, no book for him, YD 384283 doesn't even mention his name.)