  We investigate the star formation histories (SFHs) of high redshift (3 <~ z
<~ 5) star-forming galaxies selected based on their rest-frame ultraviolet (UV)
colors in the CANDELS/GOODS-S field. By comparing the results from the
spectral-energy-distribution-fitting analysis with two different assumptions
about the SFHs --- i.e., exponentially declining SFHs as well as increasing
ones, we conclude that the SFHs of high-redshift star-forming galaxies increase
with time rather than exponentially decline. We also examine the correlations
between the star formation rates (SFRs) and the stellar masses. When the
galaxies are fit with rising SFRs, we find that the trend seen in the data
qualitatively matches the expectations from a semi-analytic model of galaxy
formation. The mean specific SFR is shown to increase with redshift, also in
agreement with the theoretical prediction. From the derived tight correlation
between stellar masses and SFRs, we derive the mean SFH of star-forming
galaxies in the redshift range of 3 <~ z <~ 5, which shows a steep power-law
(with power alpha = 5.85) increase with time. We also investigate the formation
timescales and the mean stellar population ages of these star-forming galaxies.
Our analysis reveals that UV-selected star-forming galaxies have a broad range
of the formation redshift. The derived stellar masses and the stellar
population ages show positive correlation in a sense that more massive galaxies
are on average older, but with significant scatter. This large scatter implies
that the galaxies' mass is not the only factor which affects the growth or star
formation of high-redshift galaxies.
