A model based on the Quasi-Determinism theory is used in this paper to evaluate the most probable extreme excitations and their time histories on a 3-degree-of-freedom (i.e. surge, heave and pitch motions) model of a floating spar-type 5 MW wind turbine. Numerical simulations of forces in the time domain on the hull and tower of the structure have been carried out using FAST, accounting for the hydrodynamic characteristics of the floater by means of WAMIT. Sea wave forces and joint wave and wind forces have been calculated, under the hypothesis of typical wave surface elevation and wind velocity power density functions. In particular, different case studies have been chosen accounting for operational conditions of significant wave height and wind speed in a site in the Atlantic Ocean. An approach based on the Quasi-determinism theory is then used in order to assess, for each case study, the time history of all the components of the excitations when the maximum of one component of the forces occurs. Studies about the validity of the model and the qualitative and quantitative anomaly of the simulations with respect to the herein presented approach are also included.