I am aware of the classical work by Smale and Barden computing the diffeomorphism type of smooth simply connected 5-manifolds in D. Barden, [Simply connected five-manifolds](https://www.jstor.org/stable/1970702), Ann. of Math. (2) 82 (1965), 365–385 and S. Smale, [On the structure of 5-manifolds](https://www.jstor.org/stable/1970417), Ann. of Math. (2) 75 (1962), 38–46. 

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