We derive H{\alpha} fluxes for a large spectroscopic and photometric-redshift-selected sample of sources over GOODS-North and South in the redshift range z = 3.8-5.0 with deep HST, Spitzer/IRAC, and ground-based observations. The H{\alpha} flux is inferred based on the offset between the IRAC 3.6 {\mu}m flux and that predicted from the best-fit SED. We demonstrate that the H{\alpha} flux correlates well with dust- corrected UV star-formation rate (SFR) and therefore can serve as an independent SFR indicator. However, we also find a systematic offset in the SFR_H{\alpha}/SFR_UV ratios for z ~ 4-5 galaxies relative to local relations (assuming the same dust corrections for nebular regions and stellar light). We show that we can resolve the modest tension in the inferred SFRs by assuming bluer intrinsic UV slopes (increasing the dust correction), a rising star-formation history or assuming a low metallicity stellar population with a hard ionizing spectrum (increasing the L_H{\alpha}/SFR ratio). Using H{\alpha} as a SFR indicator, we find a normalization of the star formation main sequence in good agreement with recent SED-based determinations and also derive the SFR functions at z ~ 4-8. In addition, we assess for the first time the burstiness of star formation in z ~ 4 galaxies on <100 Myr time scales by comparing UV and H{\alpha}-based sSFRs; their one-to-one relationship argues against significantly bursty star-formation histories. Further progress will be made on these results, by incorporating new results from ALMA to constrain the dust-obscured star formation in high-redshift UV-selected samples.