The paper includes a construction of all the non-isomorphic greedoids on at most 5 elements in five classes of interval greedoids: local poset greedoids, poset greedoids, undirected branching greedoids, directed branching greedoids and convex shellings. A computer-aided search on the formerly generated [3] catalogue of all the non-isomorphic interval greedoids on at most 5 elements was performed for the extraction of the greedoids in the first two classes. The remaining three classes were constructed :by hand", on the basis of some more general theoretical considerations (which are not restricted to the sets consisting of at most 5 elements).