  We furnish a supersymmetric extension of the Standard Model with a flavour
discrete symmetry $A_5$ under which the lepton fields transform as an
irreducible triplet. Additional (`flavon') superfields are used to break $A_5$
into a $\mathbb{Z}_2 \times \mathbb{Z}_2$ subgroup in the charged-lepton sector
and another $\mathbb{Z}_2$ subgroup in the neutrino sector. The first column of
the resulting lepton mixing matrix is predicted and has entries which are
related to the golden ratio. Using the observed $\theta_{13}$ as input, our
model predicts a solar mixing angle $\theta_{12}$ in very good agreement with
experiment; it also predicts a correlation between the atmospheric mixing angle
$\theta_{23}$ and the $CP$-violating Dirac phase $\delta$.
