I  am  aware  of  the  classical  work  by Smale  and  Barden computing the  diffemorsphism  type  of  smooth  simply  connected  5-manifolds in   Barden. Simply connected five-manifolds, Ann. of Math. (2) 82 (1965), 365–385  and S. Smale, On the structure of 5-manifolds, Ann. of Math. (2) 75 (1962), 38–46. 

¿Is there  been  any effort  to  give  invariants  for  5-dimensional  smooth  manifolds fibering  over  a fixed  hyperbolic  surface?