Is it normal for a five week old baby to cry on end?
Yes its normal because your baby might be experiencing what is called Colic.
Babies with colic or infantile colic are healthy, well-fed babies who cry long, often inconsolable for no apparent reasons in the first three months of life.
It is often described by the rules of threes. Any healthy, well-fed infant who cries:

* More than 3 hours a day

* More than 3 days a week

* for more than 3 weeks.


Colic is common. It usually starts a few weeks after birth and often improves by age 3 months. By ages 4 to 5 months, the majority of babies with colic have improved.
Colic improves on its own, often by age 3 months. Unfortunately, there are no proven treatments that consistently help every baby.