I believe that since salat has been revealed before the Quranic Revelation, one has to look to the previous people/ Scriptures whom Salat has been revealed to, in order to get more understanding of what Salat really is, and the numbers.
The focus groups would be (All of which are mentioned/alluded to in the Quran are:
1) Mandaeans (Sabaens) (5 prayers lessened to 3 Prayers by John the Baptist) (Sabaeen in Quran 22:17)
2) Zoroastrians (5 prayers) (Majus in Quran 22:17)
3) Samaritans (3 times, more on holidays) (Early schism of children of Israel)
4) Early Jewish tribes/Torah/Tanakh (some 3, some 5, some combine 5 into 3 times)
5) New Testament (3 times, 3rd, 6th, 9th hours)
The two hardest group to find out is Mandaeans and samaritans, since their numbers are few, and there is not a lot of available literature out there.
1) This free online book is about Mandaeans
http://mandaeannetwork.com/Mandaean/en_The_Mandaeans_of_Iraq_and_Iran_sabians_mandaeannetwork.html?i1Also as an intro to Mandaeans in english:
https://www.youtube.com/watch?v=ean-WKnw_nU2) Zoroastrianism
https://archive.org/details/ourownreligionin00millrich3) Samaritans outreach website
http://www.thesamaritanupdate.com/