As @American Muslim said in his comment:
the only thing that can substitute a verse is another verse, not a hadith (but the later part of his statement is something most scholars would reject, as Qur'an is based on tawator = many equal statements by different narrators with a sane narrator chain for each):
There is neither a verse quoting 10 sucklings not one quoting 5 sucklings and as this hadith comes along only as hadith narrated by Aisha' via 'Amrah this is a so called ahaad hadith and ahaad hadith are not accepted when it comes to Quran القرآن لا يثبت بالآحاد. Also if this was known all sahaba especially those who where reciters and readers of Quran would have mentioned it either in their reading or in a hadith. This means it would be specifically quoted in the Quran or narrated by as much sahaba needed to make the hadith mutawatir, not only by 'Aisha (May Allah be pleased with her)!
Imam A-Shafi'i is maybe the first among the 4 known mujtahideen who accepted this hadith but most (sunni) scholars -before him- rejected it because of the reasons explained above! And imam al-Laith ibn Sa'ad said:
أجمع المسلمون أن قليل الرضاع وكثيره يحرم في المهد ما يفطر الصائم
(my translation so take it carefully)
There's consensus among the Muslims that few sucklings and much of them set as haram -in the cradle- that what makes a fasting person break his fast:
This means even a few suckling (one nursing) would let the child be a mahram for the woman who fed him and the children of this woman once he grow up, as breaking fast could be by intercourse during daytime!
As this hadith is also mentioned in al Muwatta' (and therefore known by imam Malik) my answer above is based on the sharh of az-Zurqani while Imam an-Nawawi in his explanation/sharh of Sahih Muslim says -somehow defending the opinion of his madhab- that as their are many ahadith quoting a minimum number of breast-feedings: making a number of feedings a condition to become a mahram is obligatory (See for example this one on the authority of 'Aisha and in other sunnah collections by other sahaba too). Apparently this opinion has been adopted by later scholars like the Hanbali/Salafi school!
On the other hand this hadith is often used as an example of "naskh al-hukm wa-'l-tilāwa نسخ التلاوة والحكم معاً": abrogation of both ruling and wording by (some of) those scholars who accepted that Qur'an can be abrogated by sunnah. But a major Issue here still is the fact that according this narration 'Aisha (May Allah be pleased with her) has said:
...Allah's apostle (may peace be upon him) died and it was before that
time (found) in the Holy Qur'an (and recited by the Muslims)
which in my opinion supports the opinion of those who rejected this hadith and declared it as ahad! As if this was true it should have been a part in the still recited Qur'an, which is not the case! An other objection accord the scholar Said al-Kamli سعيد الكملي addressed (in this video) to this narration is that 'Aisha didn't say that our Messenger said so, this means it is unclear whether this narration of 'Aisha is really a hadith at all!
On the other hand we find in al-Muwatta' many akhbar of the sahaba who were -apparently- still practicing the 10 suckling rule among them 'Aisha see for example this narration and this!
Finally scholars have based their fatwa on this Verse:
Prohibited to you [for marriage] are ..., your [milk] mothers who
nursed you, your sisters through nursing, ...
