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 (S) over cap 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, gamma, of charge 8/3 whose striking decay channel gamma -> W(+)W(+)W(+)b can lead to either exclusion or confirmation of the model in the near future.