Have worked in restaurants most of my life, and from personal experience, the most days max for a boiled egg is 4.
How Long Can Boiled Eggs And Egg Salad Stay Fresh In The Refrigerator?
With anything freshly made like egg salad I would not leave it any longer than 3 or 4 days. Anything without preservatives will tend to break down more quickly so you want to make sure to eat it in a timely fashion so you don't get sick.
IF I eat an hard boiled egg that is ten days old will I die