  We derive the complete five-gluon scattering amplitude at tree level, within
the context of Open Superstring theory. We find the general expression in terms
of kinematic factors, and also find its complete expansion up to ${\cal
O}({\alpha'}^3)$ terms. We use our scattering amplitude to test three
non-equivalent ${\cal O}({\alpha'}^3)$ effective lagrangians that have recently
been matter of some controversy.
