Timing the earliest quenching events with a robust sample of massive
  quiescent galaxies at 2 < z < 5
  We present a sample of 151 massive ($M_* > 10^{10}\mathrm{M_\odot}$)
quiescent galaxies at $2 < z < 5$, based on a sophisticated Bayesian spectral
energy distribution fitting analysis of the CANDELS UDS and GOODS-South fields.
Our sample includes a robust sub-sample of 61 objects for which we confidently
exclude low-redshift and star-forming solutions. We identify 10 robust objects
at $z>3$, of which 2 are at $z>4$. We report formation redshifts, demonstrating
that the oldest objects formed at $z > 6$, however individual ages from our
photometric data have significant uncertainties, typically $\sim0.5$ Gyr. We
demonstrate that the UVJ colours of the quiescent population evolve with
redshift at $z>3$, becoming bluer and more similar to post-starburst galaxies
at lower redshift. Based upon this we construct a model for the time-evolution
of quiescent galaxy UVJ colours, concluding that the oldest objects are
consistent with forming the bulk of their stellar mass at $z\sim6-7$ and
quenching at $z\sim5$. We report spectroscopic redshifts for two of our objects
at $z=3.440$ and $3.396$, which exhibit extremely weak Ly$\alpha$ emission in
ultra-deep VANDELS spectra. We calculate star-formation rates based on these
line fluxes, finding that these galaxies are consistent with our quiescent
selection criteria, provided their Ly$\alpha$ escape fractions are $>3$ and
$>10$ per cent respectively. We finally report that our highest-redshift robust
object exhibits a continuum break at $\lambda\sim7000$A in a spectrum from
VUDS, consistent with our photometric redshift of
$z_\mathrm{phot}=4.72^{+0.06}_{-0.04}$. If confirmed as quiescent this object
would be the highest-redshift known quiescent galaxy. To obtain stronger
constraints on the times of the earliest quenching events, high-SNR
spectroscopy must be extended to $z\gtrsim3$ quiescent objects.
