  With the help of the parametric solution of the Maxwell equal area law for
the Gauss-Bonnet AdS black hole in five dimensions, we find the second
analytical solution to the first order phase transition. We analyze the
asymptotic behaviors of some characteristic thermodynamic properties for the
small and large black holes at the critical and zero temperatures and also
calculate the critical exponents and the corresponding critical amplitudes in
detail. Moreover, we give the general form of the thermodynamic scalar
curvature based on the Ruppeiner geometry and point out that the attractive
interaction dominates in both the small and large black hole phases when the
first order phase transition occurs in the five dimensional Gauss-Bonnet AdS
black hole.
