Al-Tirmidhi, "Al-Jami' al-Sahih" (1), and that Abu Tahir al-Silafi said regarding the five books: the scholars of the East and the West have agreed upon their authenticity. Ibn al-Salah said: This is leniency, because among them there are [hadiths] which they explicitly declared to be weak, or rejected (munkar), or similar descriptions of weakness.

Ibn al-Salah was seconded in this by al-'Iraqi, who said in his "Alfiyyah":
"Whoever absolutely calls them 'Sahih' … has indeed committed clear leniency."

Some scholars have undertaken to justify the application of the designation "Sahih" (sound) to them on the basis that it is according to the predominant [portion]. Al-Zarkashi said in his notes on Ibn al-Salah (2): The naming of the three books as "Sahih" is according to the predominant, because the majority of their contents are sound (sahih) and good (hasan), and these are attached to the sound, and whatever weak [hadiths] are in them may perhaps be elevated to the level of hasan. Thus, applying the term "sound" to them is by way of predominance.

Al-Hafiz (3) said in explaining the statement of al-Hakim: He ruled for all of them as sound by virtue of predominance.

Al-Nawawi likewise explained it, saying following the statement of al-Silafi (4): His intent is that most of it—

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(1) Al-Hafiz mentioned in "Al-Nukat 'ala Ibn al-Salah" 1/481 that al-Hakim also applied the designation "sound" to the books of al-Nasa'i and Abu Dawud, and that Abu 'Ali al-Naysaburi, Ibn 'Adi, al-Daraqutni, Ibn Mandah, 'Abd al-Ghani ibn Sa'id, Abu Ya'la al-Khalili, and others applied the designation "sound" to the book of al-Nasa'i.
(2) As transmitted from him by al-Suyuti in the introduction to "Zahr al-Ruba 'ala al-Mujtaba."
(3) In "Al-Nukat 'ala Ibn al-Salah" 1/479.
(4) As transmitted from him by al-Hafiz in "Al-Nukat" 1/489, and by al-Suyuti in the introduction to "Zahr al-Ruba."