||Given a closed n-dimensional manifold whose fundamental group is $\mathbb Z$, when is M a fiber bundle over the circle $S^1$? This is a problem of theoretical importance in the study of high dimensional manifolds. A classical result of Browder-Levine gives a necessary and sufficient condition when the dimension $n \ge 6$. In this talk I will discuss a solution of this problem for $n=5$ from the point of view of classification. In the topological category, we will see that the Browder-Levine condition is still true and in the smooth category there will be further obstructions related to the topology of smooth 4-manifolds. This is a joint work with M.Kreck.