One of the intrinsic properties of proteins is their capacity to interact selectively with other molecules in their environment, inducing many chemical equilibria each differentiated by the mutual affinities of the components. A comprehensive understanding of these molecular binding processes at atomistic resolution requires formally the complete description of the system dynamics and statistics at the relevant time scales. While solution NMR observables are averaged over different time scales, from picosecond to second, recent new molecular dynamics protocols accelerated considerably the simulation time of realistic model systems. Based on known ligands recently discovered either by crystallography or NMR for the human peroxiredoxin 5, their affinities were for the first time accurately evaluated at atomistic resolution comparing absolute binding free-energy estimated by funnel-metadynamics simulations and solution NMR experiments. In particular, free-energy calculations are demonstrated to discriminate two closely related ligands as pyrocatechol and 4-methylpyrocathecol separated just by 1 kcal/mol in aqueous solution. The results provide a new experimental and theoretical basis for the estimation of ligand-protein affinities.