I googled a lot, but I did not found an answer to that question.
The first three normal forms are common sense. They are used to save consistency and avoid anamalies. But why do we need the BCNF and the fourth normal form?
(the fifth I do not even dare to ask, because I do not even understand what it does)
On
The benefits of any normal form are data integrity and a database design that concisely and accurately models a given set of business rules. 3NF and 4NF are not particularly important or useful. BCNF and 5NF are important. BCNF is concerned with enforcing the right set of functional dependencies; 5NF is concerned with enforcing the right set of join dependencies.
as commented by nvogel
The benefit of conforming to BCNF or 4NF is very similar to the benefit of conforming to 2NF or 3NF. It eliminates some harmful redundancy, and thereby prevents certain cases where the database contradicts itself.
It's a rare case where a table can be in 3NF but fail to be in BCNF or 4NF. But they do occur, and they are documented in full descriptions of the normal forms.
For example, see this description: https://en.wikipedia.org/wiki/Boyce%E2%80%93Codd_normal_form This description shows a table that is in 3NF but not BCNF.
How much effort you should expend in making sure a design conforms to BCNF or 4NF depends on the nature of your project. There are many design situations where checking for conformance to 3NF is good enough.