  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 $z\sim0.1$ 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
\citet{henriques2015} 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.
