  Let X be a supersingular K3 surface in characteristic 5 with Artin invariant
1. Then X has a polarization that realizes X as the Fermat sextic double plane.
We present a list of polarizations of X with degree 2 whose intersection number
with this Fermat sextic polarization is less than or equal to 5, and give the
defining equations of the corresponding projective models. We also present a
method to describe birational morphisms between these projective models
explicitly. As a by-product, a non-projective automorphism of the Fermat sextic
double plane is obtained.
