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Intermolecular interactions in the van der Waals bonded benzene crystal are studied from first principles, by combining exact exchange energies with correlation energies defined by the adiabatic connection fluctuation-dissipation theorem, within the random phase approximation. Correlation energies are evaluated using an iterative procedure to compute the eigenvalues of dielectric matrices, which eliminates the computation of unoccupied electronic states. Our results for the structural and binding properties of solid benzene are in very good agreement with experimental results and show that the framework adopted here is a very promising one to investigate molecular crystals and other condensed systems bound by dispersion forces.