All perfect praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
This isn`t a Hadith of the Prophet (Peace and blessings be upon him) since the scholars of Hadith didn`t narrate it with a Sanad (Chain of transmission) traced to the Prophet (Peace and blessings be upon him) except the narration of Al-Dailami in [Musnad Al-Firdous, vol.2/pp.196] and Ibn Asaker in [Tareekh Al-Sham, vol.10/pp.408] Among the Sanad of the Hadith is Ibraheem Ibn Abi Yahia and others and all of these are suspected. Therefore, Ibn Hajar regarded it as Da`if (Unreliable Hadith) in his book [Al-Talkhees Al-Hobair.]
However, scholars narrated this text from what some of the companions and successors (Tabi`een) have said. Thus, Abdulrazaq reported it in the "Mosannaf, V.4/P.317/No.7927" from what Ibn Omar said. Similarly, al-Baihaqhi reported it in [Al-Sunnan Al-Kubra, vol.3/pp.319/No.6087] from what Abi Al-Darda`s said. However, their Sanad is weak as well.
Imaam Ash-Shaafi‘i (May Allah have mercy on him) made this statement in his book [Al-Umm, vol.1/pp.264] with the following wording: “We were informed that it used to be said: "The supplications are answered on five nights: the night of Friday, the night of Al-Adhha, the night of Al-Fitr, the first night of Rajab and the night of the middle of Sha‘baan." Ar-Rabee‘ said: "Ash-Shaafi‘i said: Ibraheem ibn Muhammad said: "I saw the prominent elders of Madeenah come to the Masjid of the Prophet, sallallaahu ‘alayhi wa sallam, on the night of ‘Eed and supplicate Allaah and mention Allaah until one hour of the night had passed." And we were informed that Ibn ‘Umar used to pass the night of Juma‘ in worship. The night of Jama‘ is the night of Eed al-Adhha, as the next morning is the Day of Sacrifice. Ash-Shaafi’i said: I consider everything that has been reported about these nights to be commendable but not compulsory.” And Allah the Almighty Knows Best.