Is reading the following surahs proven from Sunnah?

Surah Yasin and Surah Fajr after Fajr prayer,

Surah al-Fath after Dhuhr prayer,

Surah an-Naba after Asr prayer,

Surah al-Waqiah, Surah ar- Rahman and Surah al-Hadeed after Maghrib prayer,

Surah al-Mulk and Surah as-Sajdah after Isha prayer.

Reciting the Surahs mentioned above in the way that you detailed does not have any proof from the Sunnah, except for the recital of Surah al-Mulk and Surah as-Sajdah every night.

It was narrated from Abu Hurayrah that the Prophet (ﷺ) said: “A surah from the Qur'an containing thirty verses will intercede for a man so that he will be forgiven. It is the surah Tabaarak Alathi bi yadihi’l-mulk [i.e., Surah al-Mulk].” [1]

What is meant is that a person should read it every night, act in accordance with the rulings contained in it, and believe in the information mentioned in it. It was narrated that Abd-Allah ibn Masod said: Whoever reads Surah al-Mulk every night, Allah will protect him from the torment of the grave. At the time of the Messenger of Allah (ﷺ) we used to call it al-maani’ah (that which protects). In the Book of Allah it is a surah which, whoever recites it every night has done very well.

As for Surah as-Sajdah; it has been narrated from Jabir (رضى الله عنه) that the Prophet (ﷺ) did not sleep until he had recited “Alif‑Laam‑Meem. The revelation…” [al-Sajdah 32] and “Has there not been over man a period of time…” [Al-Insaan 76] [2]

References:

[1] al-Tirmidhi, 2891; Abu Dawood, 1400; Ibn Maajah, 3786

 [2] Al-Tirmidhi, 2892