Lyman-alpha (Ly{alpha}) photons from ionizing sources and cooling radiation undergo a complex resonant scattering process that generates unique spectral signatures in high-redshift galaxies. We present a detailed Ly{alpha} radiative transfer study of a cosmological zoom-in simulation from the Feedback In Realistic Environments (FIRE) project. We focus on the time, spatial, and angular properties of the Ly{alpha} emission over a redshift range of z = 5-7, after escaping the galaxy and being transmitted through the intergalactic medium (IGM). Over this epoch, our target galaxy has an average stellar mass of $M_{rm star} approx 5 times 10^8 {rm M}_odot$. We find that many of the interesting features of the Ly{alpha} line can be understood in terms of the galaxys star formation history. The time variability, spatial morphology, and anisotropy of Ly{alpha} properties are consistent with current observations. For example, the rest frame equivalent width has a ${rm EW}_{{rm Ly}alpha,0} > 20 {rm AA}$ duty cycle of 62% with a non-negligible number of sightlines with $> 100 {rm AA}$, associated with outflowing regions of a starburst with greater coincident UV continuum absorption, as these conditions generate redder, narrower (or single peaked) line profiles. The lowest equivalent widths correspond to cosmological filaments, which have little impact on UV continuum photons but efficiently trap Ly{alpha} and produce bluer, broader lines with less transmission through the IGM. We also show that in dense self-shielding, low-metallicity filaments and satellites Ly{alpha} radiation pressure can be dynamically important. Finally, despite a significant reduction in surface brightness with increasing redshift, Ly{alpha} detections and spectroscopy of high-$z$ galaxies with the upcoming James Webb Space Telescope is feasible.
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