  In F-theory, U(1) gauge symmetries are encoded in rational sections, which
generate the Mordell-Weil group of the elliptic fibration of the
compactification space. Recently the possible U(1) charges for global SU(5)
F-theory GUTs with smooth rational sections were classified arXiv:1504.05593
[hep-th]. In this paper we utilize this classification to probe global F-theory
models for their phenomenological viability. After imposing an exotic-free MSSM
spectrum, anomaly cancellation (related to hypercharge flux GUT breaking in the
presence of U(1) gauge symmetries), absence of dimension four and five proton
decay operators and other R-parity violating couplings, and the presence of at
least the third generation top Yukawa coupling, we generate the remaining quark
and lepton Yukawa textures by a Froggatt-Nielsen mechanism. In this process we
require that the dangerous couplings are forbidden at leading order, and when
re-generated by singlet vevs, lie within the experimental bounds. We scan over
all possible configurations, and show that only a small class of U(1) charge
assignments and matter distributions satisfy all the requirements. The
solutions give rise to the exact MSSM spectrum with realistic quark and lepton
Yukawa textures, which are consistent with the CKM and PMNS mixing matrices. We
also discuss the geometric realization of these models, and provide pointers to
the class of elliptic fibrations with good phenomenological properties.
