We report the serendipitous detection in high-resolution optical spectroscopy of a strong, asymmetric Lyalpha emission line at z = 5.190. The detection was made in a 2.25 hr exposure with the Echelle Spectrograph and Imager on the Keck II telescope through a spectroscopic slit of dimensions 1" x 20". The progenitor of the emission line, J123649.2 + 621539 ( hereafter ES1), lies in the Hubble Deep Field North northwest flanking field, where it appears faint and compact, subtending just 0."3 (FWHM) with I-AB = 25.4. The ES1 Lyalpha line flux of 3.0 x 10(-17) ergs cm(-2) s(-1) corresponds to a luminosity of 9.0 x 10(42) ergs s(-1), and the line pro le shows the sharp blue cutoff and broad red wing commonly observed in star-forming systems and expected for radiative transfer in an expanding envelope. We find that the Lyalpha 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 star-bursts (typically 10(2)-10(3) km s(-1)) and compares favorably to simulations of the late-stage evolution of Lyalpha 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.