Grading: (3) This hadith is sahih, and this chain is strong (qawi); there is no harm in its narrators.
Technical note / Defect ('illah): However, there is disagreement in it from Abu Salih, who is Dhakwan al-Samman. His son Suhayl, narrating from him, made it a hadith of Abu Hurayrah (as in this narration and the one after it), while Asim bin Bahdalah narrated it from Abu Salih, from Mu'awiyah (as in narration no. 8316, coming below).
Important point: Imam al-Bukhari said (as al-Tirmidhi quoted in his "Jami'" after no. 1444): "On this matter the narration of Abu Salih from Mu'awiyah is more sound than his narration from Abu Hurayrah." Imam al-Tirmidhi followed him in "al-'Ilal al-Kabir" (p. 232), saying: "The hadith of Mu'awiyah is more likely and more sound." We say: It is possible that Abu Salih heard it from both Abu Hurayrah and Mu'awiyah and narrated it both ways, especially since Suhayl bin Abi Salih preserved his father's hadith well and had it in writing. In any case, this is a disagreement that does no harm, since both of them are eminent Companions.

Technical note / Defect ('illah): Sa'id is Ibn Abi Arubah. Abd al-Wahhab's narration from him is from before (his) mental deterioration (ikhtilat). We have not found this through the route of Sa'id bin Abi Arubah with anyone other than the author (al-Hakim).

Corroborating chains and supporting reports: Ma'mar corroborated Sa'id (as in the next narration with the author, al-Hakim), and Ibn Jurayj also corroborated him, as al-Tirmidhi mentioned in his "Jami'" after (1444).

Reference / Source: Ahmad bin Abd al-Jabbar al-Utaridi narrated it from Abu Bakr bin Ayyash, from Asim bin Bahdalah, from Abu Salih, from Abu Hurayrah, in Abu al-Bakhtari's "Majmu' Musannafatihi" (321), Ibn Shadhan's "al-Awwal min Hadithihi" (75) and Qadi al-Maristan's "al-Mashyakhah al-Kubra" (150).
Technical note / Defect ('illah): Al-Utaridi was mistaken in this by making it a hadith of Abu Hurayrah, as al-Daraqutni said in "al-'Ilal" (1222).

Technical note / Defect ('illah): What is preserved (mahfuz) in the narration of Abu Bakr bin Ayyash is what his students narrated: Abu Kurayb Muhammad bin al-Ala' (al-Tirmidhi: 1444), Uthman bin Abi Shaybah (Abu Ya'la: 7363), Abu Hisham Muhammad bin Yazid bin Rifa'ah (Abu al-Fadl al-Zuhri's "Hadithuhu": 156, and Abu Tahir al-Mukhallis's "al-Mukhallisiyyat": 1353) and Muslim bin Sallam, the mawla of Banu Hashim (as mentioned by al-Daraqutni in "al-'Ilal"). These four narrators narrate it from him (Abu Bakr), from Asim, from Abu Salih, from Mu'awiyah bin Abi Sufyan (may Allah be pleased with him). Likewise the students of Asim bin Bahdalah also narrated it from him, and the sources of the narration of Asim's students from him will come soon under the next hadith of Mu'awiyah (may Allah be pleased with him).

Note / Clarification: Caution: Ibn Hibban in his "Sahih" (4445) narrated this very hadith from Abu Ya'la himself, but made it a hadith of Abu Sa'id al-Khudri instead of Mu'awiyah. Abdullah bin Muhammad al-Baghawi also corroborated Abu Ya'la in narrating it from Uthman bin Abi Shaybah (in Ibn Shahin's "Nasikh al-Hadith wa Mansukhuhu": 527), so what is in Ibn Hibban would be a "mistake"; and Allah knows best.