Here's an example of a 4NF problem as presented in Teorey's book.
Consider the entities Employee, Skill, and Project. An employee must have all skills required for the project to work on a project. Thus there is a relation or bridge table Employee-Skill-Project. However, the Employee-Skill relationship remains regardless of the project and the employee can have skills not related to the project. The composite relation or bridge tables are Employee-Skill, Project-Skill, and Employee_Project, but this is not enough as an employee may require several skills or have worked on several projects. A model is in 4NF if all many-to-many-to-many relationships can only be decomposed into 3 many-to-many relationships.
I'm not even going to attempt to explain 5NF in this forum - sorry.
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The reasonable man adapts himself to the world. The unreasonable one persists in trying to adapt the world to himself. Therefore all progress depends on the unreasonable man. - George Bernard Shaw