Our results demonstrate that the RISM approach gives a comprehensive description of the complex interactions at the Pt(111) water interface with specifics improvement compared to Poisson-Boltzmann models. The inclusion of lone-pairs in the TIP5P model proves to be a crucial factor in capturing the essential physics of the interface, including the correct description of solvation energies, workfunctions, and the double layer structure. These findings establish a foundation for comparing RISM with AIMD studies, opening avenues for further comparative studies, including the analysis of solvent densities and charge distributions around the electrode. Further improvements such as the RISM parametrization of O and H DFT solutes, and computational stability will be needed to move towards more accurate electrochemical simulations and systematically incorporate RISM into computational studies.