We report the serendipitous detection in high–resolution optical spectroscopy of a strong , asymmetric Ly \alpha emission line at z = 5.190 . The detection was made in a 2.25 hour exposure with the Echelle Spectrograph and Imager on the Keck II telescope through a spectroscopic slit of dimensions 1″ \times 20″ . The progenitor of the emission line , J123649.2 + 621539 ( hereafter ES1 ) , lies in the Hubble Deep Field North West Flanking Field where it appears faint and compact , subtending just 0 \farcs 3 ( FWHM ) with I _ { \mbox { \tiny AB } } = 25.4 . The ES1 Ly \alpha line flux of 3.0 \times 10 ^ { -17 } ergs cm ^ { -2 } s ^ { -1 } corresponds to a luminosity of 9.0 \times 10 ^ { 42 } ergs s ^ { -1 } , and the line profile shows the sharp blue cut–off and broad red wing commonly observed in star–forming systems and expected for radiative transfer in an expanding envelope . We find that the Ly \alpha profile is consistent with a galaxy–scale outflow with a velocity of v > 300 km s ^ { -1 } . This value is consistent with wind speeds observed in powerful local starbursts ( typically 10 ^ { 2 } to 10 ^ { 3 } km s ^ { -1 } ) , and compares favorably to simulations of the late–stage evolution of Ly \alpha emission in star–forming systems . We discuss the implications of this high–redshift galactic wind for the early history of the evolution of galaxies and the intergalactic medium , and for the origin of the UV background at z > 3 .