  Low-energy data, combined with renormalization group (RG) equations, can
predict new physics at far higher energy scales. In this paper, we consider the
possibility that the measured Higgs boson mass and top quark mass hint at a
five-dimensional gauge-Higgs unification (5D GHU) model at a scale above TeV.
We note that the vanishing of the Higgs quartic coupling and the proximity of
the top quark Yukawa coupling and weak gauge coupling at high scales, inferred
from the experimental data, are in harmony with 5D GHU, because in 5D GHU
models the Higgs quartic coupling is forbidden by the 5D gauge symmetry and the
Yukawa couplings and the weak gauge coupling originate from a common 5D gauge
coupling. Based on the above insight, we propose a 5D GHU model where the
Standard Model fermions are embedded in 5D fermions in a way to tightly relate
the top Yukawa coupling with the weak gauge coupling. Also, the model predicts
the presence of vector-like fermions (other than the Kaluza-Klein modes), which
can affect the RG evolutions of the 4D theory and reconcile the scale of
vanishing Higgs quartic coupling and that of equality of the top Yukawa and
weak gauge couplings, thereby achieving a successful matching of the 4D theory
with 5D GHU. We predict the vector-like fermion mass and the compactification
scale of 5D GHU from the conditions for the successful matching.
