  We study the Geometric Langlands Conjecture (GLC) for rank two flat bundles
on the projective line $C$ with tame ramification at five points $\{p_{1},
p_{2}, p_{3}, p_{4}, p_{5} \}$. In particular we construct the automorphic
$D$-modules predicted by GLC on the moduli space of rank two parabolic bundles
on $(C, \{p_{1}, p_{2}, p_{3}, p_{4}, p_{5} \})$. The construction uses
non-abelian Hodge theory and a Fourier-Mukai transform along the fibers of the
Hitchin fibration to reduce the problem to one in classical projective geometry
on the intersection of two quadrics in $\mathbb{P}^{4}$.
