  We provide an explicit desingularization and study the resulting fiber
geometry of elliptically fibered fourfolds defined by Weierstrass models
admitting a split A_4 singularity over a divisor of the discriminant locus.
Such varieties are used to geometrically engineer SU(5) Grand Unified Theories
in F-theory. The desingularization is given by a small resolution of
singularities. The I_5 fiber naturally appears after resolving the
singularities in codimension-one in the base. The remaining higher codimension
singularities are then beautifully described by a four dimensional affine
binomial variety which leads to six different small resolutions of the the
elliptically fibered fourfold. These six small resolutions define distinct
fourfolds connected to each other by a network of flop transitions forming a
dihedral group. The location of these exotic fibers in the base is mapped to
conifold points of the threefolds that defines the type IIB orientifold limit
of the F-theory. The full resolution have interesting properties, specially for
fibers in codimension three: the rank of the singular fiber does not necessary
increase and the fibers are not necessary in the list of Kodaira and some are
not even (extended) Dynkin diagram.
