  Regular homotopy classes of immersions of a 3-sphere in 5-space constitute an
infinite cyclic group. The classes containing embeddings form a subgroup of
index 24. The obstruction for a generic immersion to be regularly homotopic to
an embedding is described in terms of geometric invariants of its self
intersection. Geometric properties of self intersections are used to construct
two invariants J and St of generic immersions which are analogous to Arnold's
invariants of plane curves. We prove that J and St are independent first order
invariants and that any first order invariant is a linear combination of these.
  As by-products, some invariants of immersions of 3-spheres in 4-space are
obtained. Using them, we find restrictions on the topology of self
intersections.
