  The electroweak phase transition in GUT inspired $SO(5) \times U(1) \times
SU(3)$ gauge-Higgs unification is shown to be of weakly first-order and occurs
at $T = T_c^{ \rm EW} \sim 163 \,$GeV, which is very similar to the behavior in
the standard model in perturbation theory. There appears a new phase at higher
temperature. $SU(2)_L \times U(1)_Y$ ($ \theta_H=0$) and $SU(2)_R \times
U(1)_{Y'}$ ($ \theta_H= \pi$) phases become almost degenerate above $T \sim
m_{\rm KK}$ where $m_{\rm KK}$ is the Kaluza-Klein mass scale typically around
13TeV and $\theta_H$ is the Aharonov-Bohm phase along the fifth dimension. The
two phases become degenerate at $T = T_c^{\rm LR} \sim m_{\rm KK}$. As the
temperature drops in the evolution of the early universe the $SU(2)_R \times
U(1)_{Y'}$ phase becomes unstable. The tunneling rate from the $SU(2)_R \times
U(1)_{Y'}$ phase to the $SU(2)_L \times U(1)_Y$ phase becomes sizable and a
first-order phase transition takes place at $T=2.5 \sim 2.6\,$TeV. It is shown
that the $W$ boson, $Z$ boson and photon, with $\theta_H$ varying from 0 to
$\pi$, are transformed to gauge bosons in the $SU(2)_R \times U(1)_{Y'}$ phase.
Gauge couplings and wave functions of quarks, leptons and dark fermions in the
$SU(2)_R \times U(1)_{Y'}$ phase are determined.
