Who knows thirty-five?
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35 gold denarii is the fine levied on one who embarrasses a Torah scholar, whether by word or by action. (Rambam, Hil. Chovel Umazik 3:5)
Rambam goes on to say (ibid. :6) that he witnessed such rulings being handed down in his native Spain (in the 12th century). However, Rema (Yoreh De'ah 243:7) cites later authorities (from the 14th-15th centuries) who say that today there are no longer any scholars of such stature, and that therefore this rule is no longer applied (although a beis din should still impose other penalties for such behavior).
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 283:1 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 283 doesn't even mention his name.)
35 are the soldiers of the haganah who were killed on January 16th, 1948 while traveling on foot to reinforce and resupply the Gush Etzion kibbutzim.
35 is the age at which someone whose body hasn't manifested the physical signs of maturity is considered a "סריס חמה" even though they don't otherwise have the physical symptoms of being a סריס חמה. From Yevamos 97a:
שמע מינה וכי לא נולדו לו סימני סריס עד כמה תני דבי רבי חייא עד רוב שנותיו
which is interpreted by Maimonides in הלכות אישות 2:11 to be 35 years old.
35 are the entries in Megillat Ta'anit.
Yehoshafat was thirty five years old when he was anointed King (Melachim1 22:42)
יְהוֹשָׁפָט בֶּן שְׁלשִׁים וְחָמֵשׁ שָׁנָה בְּמָלְכוֹ
Thirty-five Words in "ויכולו" and Thirty-five Words in the Beracha of Kiddush
The Talmud (Kiddushin 71a) also limits who may be taught the forty-two-letter esoteric Name of God. Rav warns that it should only be taught to a person who is modest, humble, is not easily angered, does not get drunk and does not hold a grudge; additionally, he must be at “half his years,” understood by Rashi in Sanhedrin to mean thirty-five years old.