  We consider the standard model (SM) extended by the flavor symmetry D5 and
search for a minimal model leading to viable phenomenology. We find that it
contains four Higgs fields apart from the three generations of fermions whose
left- and left-handed conjugate parts do not transform in the same way under
D5. We provide two numerical fits for the case of Dirac and Majorana neutrinos
to show the viability of our low energy model. The fits can accommodate all
data with the neutrinos being normally ordered. For Majorana neutrinos two of
the right-handed neutrinos are degenerate. Concerning the Higgs sector we find
that all potentials constructed with three SM-like Higgs doublets transforming
as 1+2 under D5 have a further unwanted global U(1) symmetry. Therefore we
consider the case of four Higgs fields forming two D5 doublets and show that
this potential leads to viable solutions in general, however it does not allow
spontaneous CP-violation (SCPV) for an arbitrary vacuum expectation value (VEV)
configuration. Finally, we discuss extensions of our model to grand unified
theories (GUTs) as well as embeddings of D5 into the continuous flavor
symmetries SO(3)_f and SU(3)_f.
