A relation is in 5NF if it is in 4NF and not contains any join dependency and joining should be lossless.
5NF is satisfied when all the tables are broken into as many tables as possible in order to avoid redundancy.
5NF is also known as Project-join normal form (PJ/NF).
Example
SUBJECT
LECTURER
SEMESTER
Computer
Anshika
Semester 1
Computer
John
Semester 1
Math
John
Semester 1
Math
Akash
Semester 2
Chemistry
Praveen
Semester 1
In the above table, John takes both Computer and Math class for Semester 1 but he doesn't take Math class for Semester 2. In this case, combination of all these fields required to identify a valid data.
Suppose we add a new Semester as Semester 3 but do not know about the subject and who will be taking that subject so we leave Lecturer and Subject as NULL. But all three columns together acts as a primary key, so we can't leave other two columns blank.
So to make the above table into 5NF, we can decompose it into three relations P1, P2 & P3: