  We propose a renormalisable model based on $A_4$ family symmetry with an
$SU(5)$ grand unified theory (GUT) which leads to the minimal supersymmetric
standard model (MSSM) with a two right-handed neutrino seesaw mechanism.
Discrete $\mathbb{Z}_9\times \mathbb{Z}_6$ symmetry provides the fermion mass
hierarchy in both the quark and lepton sectors, while $\mathbb{Z}_4^R$ symmetry
is broken to $\mathbb{Z}_2^R$, identified as usual R-parity. Proton decay is
highly suppressed by these symmetries. We discuss both the $A_4$ and $SU(5)$
symmetry breaking sectors, including doublet-triplet splitting, Higgs mixing
and the origin of the $\mu$ term. The model provides an excellent fit (better
than one sigma) to all quark and lepton (including neutrino) masses and mixing
with spontaneous CP violation. With the $A_4$ vacuum alignments, $(0,1,1)$ and
$(1,3,1)$, the model predicts the entire PMNS mixing matrix with no free
parameters, up to a relative phase, selected to be $2\pi/3$ from a choice of
the nine complex roots of unity, providing a direct link between neutrino
oscillations and leptogenesis.
