There's not too much danger in eating 5 eggs at once, but I wouldn't suggest it if you are not doing much exercise.
If you think of how people naturally ate in the wild, they would eat large amounts at a time, and if they were eating animal protein, such as meat or eggs, they would eat a fair bit of it at a time - if you caught an animal, you would eat the whole thing in a meal as in the wild you didn't have a fridge.
Fruit and vegetables on the other hand you could understand that people would come across often, just picking them from trees and stuff. Not much effort required, but you only get fruit and vegetables.
In the natural system though, you could only get a large animal protein meal after you have gone to some intense physical effort to catch the animal, kill it and drag it back to the camp. You are then rewarded with a high protein meal.
Little or no exercise = fruit and vegetables, not much animal protein.
Intense physical exercise = big meal of animal protein.
Where people get fat is when they make little or no exercise = big meal of animal protein (plus other refined, chemical laden stuff).
Good to hear that you support free-range eggs by the way.