  We study low energy implications of F-theory GUT models based on $SU(5)$
extended by a $U(1)'$ symmetry which couples non-universally to the three
families of quarks and leptons. This gauge group arises naturally from the
maximal exceptional gauge symmetry of an elliptically fibred internal space, at
a single point of enhancement, $E_8\supset SU(5)\times SU(5)'\supset
SU(5)\times U(1)^4$. Rank-one fermion mass textures and a tree-level top quark
coupling are guaranteed by imposing a $Z_2$ monodromy group which identifies
two abelian factors of the above breaking sequence. The $U(1)'$ factor of the
gauge symmetry is an anomaly free linear combination of the three remaining
abelian symmetries left over by $Z_2$. Several classes of models are obtained,
distinguished with respect to the $U(1)'$ charges of the representations, and
possible extra zero modes coming in vector-like representations. The
predictions of these models are investigated and are compared with the LHC
results and other related experiments. Particular cases interpreting the
B-meson anomalies observed in LHCb and BaBar experiments are also discussed.
