We analyze the non-standard mixing history of the solar twins HIP 55459, HIP 79672, HIP 56948, HIP 73815, and HIP 100963, to determine as precisely as possible their mass and age. We computed a grid of evolutionary models with non-standard mixing at several metallicities with the Toulouse-Geneva code for a range of stellar masses assuming an error bar of +/-50K in Teff. We choose the evolutionary model that reproduces accurately the observed low lithium abundances observed in the solar twins. Our best-fit model for each solar twin provides a mass and age solution constrained by their Li content and Teff determination. HIP 56 948 is the most likely solar-twin candidate at the present time and our analysis infers a mass of 0.994+/-0.004M_{sun}_ and an age of 4.71+/-1.39Gyr. Non-standard mixing is required to explain the low Li abundances observed in solar twins. Li depletion due to additional mixing in solar twins is strongly mass dependent. An accurate lithium abundance measurement and non-standard models provide more precise information about the age and mass more robustly than determined by classical methods alone.