  We present \emph{area (or entropy) functional relation} for multi-horizons
five dimensional (5D) Einstein-Maxwell-Gauss-Bonnet-AdS Black Hole. It has been
observed by exact and explicit calculation that some complicated function of
two or three horizons area is \emph{mass-independent} whereas the entropy
product relation is \emph{not} mass-independent. We also study the local
thermodynamic stability of this black hole. The phase transition occurs at
certain condition. \emph{Smarr mass formula} and \emph{first law} of
thermodynamics have been derived. This \emph{mass-independent} relation
suggests they could turn out to be an \emph{universal} quantity and further
helps us to understanding the nature of black hole entropy (both interior and
exterior) at the microscopic level. In the \emph{Appendix}, we have derived the
thermodynamic products for 5D Einstein-Maxwell-Gauss-Bonnet black hole with
\emph{vanishing} cosmological constant.
