We introduce a version of Heegaard diagrams for 5-manifolds, which we use to study closed 5-manifolds as well as 4-manifolds and cobordisms between them. As an application, we study Heegaard diagrams of 5-dimensional cobordisms from the standard 4-sphere to Gluck twists along knotted 2-spheres. This gives some equivalent statements to Gluck twists being diffeomorphic to the standard 4-sphere.