We extend the classification of the free fermionic heterotic–string vacua to models in which the SO(10) GUT symmetry at the string scale is broken to the flipped SU(5) subgroup. In our classification method, the set of basis vectors defined by the boundary conditions which are assigned to the free fermions is fixed and the enumeration of the string vacua is obtained in terms of the Generalized GSO (GGSO) projection coefficients entering the one–loop partition function. We derive algebraic expressions for the GGSO projections for all the physical states appearing in the sectors generated by the set of basis vectors. This enables the analysis of the entire string spectrum to be programmed in to a computer code therefore, we performed a statistical sampling in the space of 2^{44} ≈ 10^{13} flipped SU(5) vacua and scanned up to 10^{12} GGSO configurations. For that purpose, two independent codes were developed based on JAVA and FORTRAN95. All the results presented are confirmed by the two independent routines. Contrary to the corresponding Pati–Salam classification, we do not find exophobic flipped SU(5) vacua with an odd number of generations.