Using observed stellar mass functions out to z = 5 , we measure the main progenitor stellar mass growth of descendant galaxies with masses of \log { M _ { * } / M _ { \odot } } = 11.5 , 11.0 , 10.5 , 10.0 at z \sim 0.1 using an evolving cumulative number density selection . From these mass growth histories , we are able to measure the time at which half the total stellar mass of the descendant galaxy was assembled , t _ { a } , which , in order of decreasing mass corresponds to redshifts of z _ { a } = 1.28 , 0.92 , 0.60 and 0.51 . We compare this to the median light-weighted stellar age t _ { * } ( z _ { * } = 2.08 , 1.49 , 0.82 and 0.37 ) of a sample of low redshift SDSS galaxies ( from the literature ) and find the timescales are consistent with more massive galaxies forming a higher fraction of their stars ex-situ compared to lower mass descendants . We find that both t _ { * } and t _ { a } strongly correlate with mass which is in contrast to what is found in the EAGLE hydrodynamical simulation which shows a flat relationship between t _ { a } and M _ { * } . However , the semi-analytic model of Henriques et al . ( 13 ) is consistent with the observations in both t _ { a } and t _ { * } with M _ { * } , showing the most recent semi-analytic models are better able to decouple the evolution of the baryons from the dark matter in lower-mass galaxies .