In fact, if you ignore that error and save it then, Quick Base will change it automatically from AND to and.
If(
[Date of Request]>(Today()+Days(1)) and [Date of Request]<(Today()+Days(6)), "yellow",
[Date of Request]>(Today()+Days(5)) and [Date of Request]<(Today()+Days(11)), "blue",
[Date of Request]>(Today()+Days(10)), "red", "")
I don't know why it is expecting , after the AND. I will report it out separately to the QB Support team about it.
Thanks,
Gaurav