  Motivated by recent work, nonmonotonic behaviours of photon sphere radius can
be used to reflect black hole phase transition for
Reissner-Nordstr$\ddot{o}$m-AdS (RN-AdS) black holes, we study the case of
five-dimensional charged Gauss-Bonnet-AdS (GB-AdS) black holes in the reduced
parameter space. We find that the nonmonotonic behaviours of photon sphere
radius still exist. Using the coexistence line calculated from $P-V$ plane, we
capture the photon sphere radius of saturated small and large black holes (the
boundary of the coexistence phase), then illustrate the reduced coexistence
region. The results show that, reduced coexistence region decreases with charge
$Q$ but increases with Gauss-Bonnet coefficient $\alpha$. When the charge
vanishes, reduced coexistence region doesn't vary with Gauss-Bonnet coefficient
$\alpha$ any more. In this case, the Gauss-Bonnet coefficient $\alpha$ plays
the same role as the charge of five-dimensional RN-AdS black holes. Also, the
situation of higher dimension is studied in the end.
