  We discuss the options for parity assignments in (on-shell) N=2
five-dimensional Yang-Mills-Einstein supergravity theories (YMESGTs) coupled to
tensor and hypermultiplets on the orbifold spacetime M_4 X S^1/Z_2. Along the
lines of orbifold-GUTs, we allow for general breaking of the five-dimensional
gauge group at the orbifold fixed points. We then extend the discussion to the
case where the orbifold is S^1/(Z_2xZ_2). We do not presume the existence of
fields with support only at fixed points. As in the familiar case of (rigid)
super-Yang-Mills theories on such orbifolds, only bulk hypermultiplets can lead
to chiral multiplets in complex representations of the gauge group on the
boundaries. Massless chiral multiplets coming from bulk vector or tensor
multiplets can potentially be used as Higgs supermultiplets, though a
"doublet-triplet" splitting via parity assignments is not available for the
tensor sector. We also find parity assignments for objects other than fields
that appear in the Lagrangian, which will partially determine the structure of
interactions of the boundary theories. Assigning odd parities to the scalar
sector of vector/tensor multiplets requires the four-dimensional boundary
moduli spaces to lie on the boundary of the classical Kaehler cone, which
corresponds to collapsed Calabi-Yau 2-cycles at the orbifold fixed points in a
compactification of eleven-dimensional supergravity. There is an ambiguity in
how to effect odd parity for the field-independent C_(IJK) tensor of the 5D
theory, which may admit a classical interpretation as Calabi-Yau 4-cycles
collapsing to either 2- or 0-cycles.
