  The selection of red, passive galaxies in the early Universe is very
challenging, especially beyond z~3, and it is crucial to constrain theoretical
modelling of the processes responsible for their rapid assembly and abrupt
shut-down of the star formation. We present here the analysis of ALMA archival
observations of 26 out of the 30 galaxies in the deep CANDELS GOODS-South field
that we identified as passive at z~3-5 by means of a careful and conservative
SED fitting analysis. ALMA data are used to verify the potential contamination
from red, dusty but star--forming sources that could enter the sample due to
similar optical--nearIR colours. With the exception of a few marginal
detections at <3sigma, we could only infer upper limits, both on individual
sources and on the stacks. We translated the ALMA continuum measurements into
corresponding SFRs, using a variety of far-IR models. These SFRs are compared
with those predicted by secondary star-forming solutions of the optical fits
and with the expected position of the star formation Main Sequence. This
analysis confirms the passive nature of 9 candidates with high confidence and
suggests that the classification is correct for at least half of the sample in
a statistical sense. For the remaining sources the analysis remain inconclusive
because available ALMA data is not deep enough, although the stacking results
corroborate their passive nature. Despite the uncertainties, this work provides
decisive support to the existence of passive galaxies beyond z~3.
