In League of Legends multiple champions can heal other champions, I was wondering what the top 5 champions biggest heals in history have been. Is there a specific number?
This does not directly answer the question, but it's probably true anyways:
There are sites (cf. Link on bottom), that record the overall healing done, while the healing of your team mates is not recorded separately (cf. bottom Screenshot from the end statistics).
When you observe the champions, that are played by those 'record players' you will always find the same:
Considering, that Zac and Vladimir only heal themselves (if not playing some troll builds with heal items / summoner spells), you have a clear number 1, namely Soraka (followed by Sona).
For the other ranks you have to dive deeper since the 'self heal champions' supersede the 'team mate heal champions'.
(BTW: You can browse the different skill groups and you will observe the same.)
Since you asked about the history of the game, I will be referencing Athenes and Ardent censor. I found a Reddit post that puts Soraka at the highest healing possible with her W being 1,328 single target. However, this post also references Janna having the highest possible burst healing(with a 1,600+ heal with a base cooldown of 2 seconds).
Sadly in modern League of Legends, you no longer have crazy high healing numbers, but rather really high sustain over time.