  We show that, under a certain condition, contact 5-manifolds can `coarsely'
distinguish smooth structures on compact Stein 4-manifolds via contact open
books. We also give a simple sufficient condition for an infinite family of
Stein 4-manifolds to have an infinite subfamily of pairwise non-diffeomorphic
Stein 4-manifolds. The proofs rely on the adjunction inequality. We remark that
there are various examples of infinitely many pairwise exotic Stein 4-manifolds
whose smooth structures can be distinguished by these results.
