We consider the moduli space of logarithmic connections of rank 2 on the projective line minus 5 points with fixed spectral data. We compute the cohomology of such moduli space, and this computation will be used to extend the results of Geometric Langlands correspondence due to D. Arinkin to the case where the this type of connections have five simple poles on P1. In this talk, I will review the Geometric Langlands Correspondence in the tames ramified cases, and after that, I will explain how the cohomology of above moduli space will be used