There is a another chain with similar narration.
Jami` at-Tirmidhi Book 5, Hadith 6
← Previous Hadith "Umar bin Al-Khattab asked Abu Waqid Al-Laithi what Allah's Messenger would recite during Al-Fitr and Al-Adha, so he said: 'He would recite: Qaf, By the Glorious Quran and the Hour has drawn near, and the moon has been cleft asunder.'"

Jami` at-Tirmidhi Book 5, Hadith 5 Next Hadith → "The Prophet said the Takbir in the first (Rak'ah) sever (times) before the recitation, and in the last, five (times) before the recitation."

Jami` at-Tirmidhi Book 5, Hadith 7