  We construct and study the 5D realization of a composite Higgs model with
minimal tuning. The Higgs is a (pseudo-)Goldstone boson from the spontaneous
breaking of a global SO(5) symmetry to an SO(4) subgroup. The peculiarity of
our construction lies in the specific choice of the SO(5) representations of
the 5D fermions from which the Standard Model fields arise as chiral zero
modes. This choice reduces the tuning of these models to the minimal
model-independent value allowed by electroweak precision tests. We analyse the
main differences between our 5D construction and other descriptions in terms of
purely 4D field theories. 5D models are generally more constrained and show a
generic difficulty in accommodating a light Higgs without reintroducing large
corrections to the \hat{S} parameter. We propose a specific construction in
which this tension can be, even though accidentally, relaxed. We discuss the
spectrum of the top partners in the viable regions of parameter space and
predict the existence of light exotic quarks, \Upsilon, of charge 8/3 whose
striking decay channel \Upsilon\to W^+W^+W^+ b can lead to either exclusion or
confirmation of the model in the near future.
