  The Hayward metric is a spherically symmetric charged regular black holes, a
modification of the Reisnner-Nordstr$\ddot{o}$m black holes of Einstein's
equations coupled to nonlinear electrodynamics. We consider
Einstein-Gauss-Bonnet gravity (EGB) coupled to nonlinear electrodynamics to
present an exact five dimension ($5D$) Hayward black holes with a regular
center, having inner (Cauchy) and outer (event) horizons which go over to
Boulware-Desser black holes when the charge is switched off ($e=0$). The
presence of charge $e$ leads the modification in thermodynamical quantities,
and it has also been shown that the Hawking-Page like phase transition can be
achieved. The specific heat shows divergence at the horizon radius $r=r_C$
(critical radius), where the temperature has a maximum. Our result in the
limit, $e\to0$, reduces vis-a-vis to the $5D$ Boulware-Desser solutions.
