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.
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