  In a recent paper, we identified a cosmological sector of a flipped $SU(5)$
model derived in the free fermionic formulation of the heterotic superstring,
containing the inflaton and the goldstino superfields with a superpotential
leading to Starobinsky type inflation, while $SU(5){\times}U(1)$ is still
unbroken. Here, we study the properties and phenomenology of the vacuum after
the end of inflation, where the gauge group is broken to the Standard Model. We
identify a set of vacuum expectation values, triggered by the breaking of an
anomalous $U(1)_A$ gauge symmetry at roughly an order of magnitude below the
string scale, that solve the F and D-flatness supersymmetric conditions up to
6th order in the superpotential which is explicitly computed, leading to a
successful particle phenomenology. In particular, all extra colour triplets
become superheavy guaranteeing observable proton stability, while the Higgs
doublet mass matrix has a massless pair eigenstate with realistic hierarchical
Yukawa couplings to quarks and leptons. The supersymmetry breaking scale is
constrained to be high, consistent with the non observation of supersymmetric
signals at the LHC.
