  In the present work, we consider a charged black hole in five dimensional
Einstein-Gauss-Bonnet gravity where the {\alpha} corrected entropy term is
considered. We examine the horizon radii product, entropy product, Hawking
temperature product and free energy product for both event horizon and Cauchy
horizon. Our motive is to check whether the same quantity for event horizon and
Cauchy horizon is free of mass, i.e., global or not. We further study the
stability of such black hole by computing the specific heat and free energy for
both the horizons. All these calculation might be helpful to understand the
microscopic nature of such black holes.
