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Motivated by experimental measurements indicating deviations from theStandard Model predictions we discuss F-theory inspired models, which, inaddition to the three chiral generations contain a vector-like complete fermionfamily. The analysis takes place in the context of $SU(5)\times U(1)'$ GUTembedded in an $E_8$ covering group which is associated with the (highest)geometric singularity of the elliptic fibration. In this context, the $U(1)'$is a linear combination of four abelian factors subjected to appropriateanomaly cancellation conditions. Furthermore, we require universal $U(1)'$charges for the three chiral families and different ones for the correspondingfields of the vector-like representations. Under the aforementionedassumptions, we find 192 such models which can be classified into five distinctcategories with respect to their specific GUT properties. We exhibitrepresentative examples for each such class and construct the superpotentialcouplings and the fermion mass matrices. We explore the implications of thevector-like states in low energy phenomenology including the predictionsregarding the B-meson anomalies. The r\^ole of R-parity violating termsappearing in some particular models of the above construction is alsodiscussed.

$SU(5)\times{U(1)'}$ models with a vector-like fermion family