On a smooth quintic 4-fold

The birational geometry of an arbitrary smooth quintic 4-fold is studied using the properties of log pairs. As a result, a new proof of its birational rigidity is given and all birational maps of a smooth quintic 4-fold into fibrations with general fibre of Kodaira dimension zero are described.
In the Addendum similar results are obtained for all smooth hypersurfaces of degree $n$ in $\mathbb P^n$ in the case of $n$ equal to 6, 7, or 8.