  We consider a supersymmetric SU(5) model where two neutrino masses are
obtained via a mixed type I+III seesaw mechanism induced by the component
fields of a single SU(5) adjoint. We have analyzed the phenomenology of the
model paying particular attention to flavour violating processes and dark
matter relic density, assuming universal boundary conditions. We have found
that, for a seesaw scale larger than $10^{12\div 13}$ GeV, BR$(\mu\to e
\gamma)$ is in the reach of the MEG experiment in sizable regions of the
parameter space. On the other side, current bounds on it force BR$(\tau \to \mu
\gamma)$ to be well below the reach of forthcoming experiments, rendering thus
the model disprovable if a positive signal is found. The same bounds still
allow for a sizable positive contribution to $\epsilon_K$, while the CP
violation in the $B_s$ mixing turns out to be too small to account for the
di-muon anomaly reported by the D0 collaboration. Finally, the regions where
the neutralino relic density is within the WMAP bounds can be strongly modified
with respect to the constrained MSSM case. In particular, a peculiar
coannihilation region, bounded from above, can be realized, which allows us to
put an upper bound on the dark matter mass for certain set-ups of the
parameters.
