I remember seeing this on broadcast TV, where, in addition to the part where he drinks five eggs before jogging slowly through the city, about 70 minutes in, he drinks EIGHT eggs before he runs through the city with the "gonna fly now" music, about 90 minutes in.
I'd love to see that again; it was a real contrast.
Not sure if I know where to find this version but here's the scene if you just gotta see it.
I counted 5 eggs...
https://www.youtube.com/watch?v=snqs566G_Zg
I think OP is suffering from the so called Mandela Effect.
I never got the whole idea of eating/drinking raw eggs bit - is there an advantage? They're slimy and disgusting and it only takes minutes to cook them into something delicious, and there's no loss of protein or essential fatty acids from the cooking process. Medical sites say that boiled eggs actually make more protein available to the body than raw.
https://www.webmd.com/diet/health-benefits-raw-eggs
https://www.mysportscience.com/post/is-it-better-for-muscle-building-to-eat-eggs-raw
Drinking raw eggs is outdated. Protein powders became widely available in the 1980s, make it easier to consume a lot of protein quickly, but prior to that, this is how it was done. I'm bringing this so that you realize that the raw egg drink was used back than the was protein shakes are used by athletes now. It wasn't replace a meal, but to supplement it. Rocky was drinking them as soon as he woke up, he would probably still eat cooked eggs as breakfast after his morning training.
Athletes need to squeeze a lot protein in. The typical recommendation is 1 gram per pound of bodyweight. Rocky is supposed to be a heavy weight, which would be over 200lbs. The 5 raw eggs is only 30 grams of protein. He would probably have to do this twice a day, in addition to his 3-4 meal to get to 200 grams a day.
To answer you question is there an advantage. It's much quicker to crack them into a glass and quickly drink them, than it would be to cook them and then sit down and eat them. Its also easier to consume things by drinking them, rather than eating them.