  Aims. We present a determination of the intrinsic colors and ages of galaxies
at very high redshift, in particular old galaxies (OGs) within extremely red
objects (EROs). To date, the definition of EROs has been restricted to objects
with z<2.5, however, here consider objects with the same properties but shifted
to higher redshifts (z>2.5). We therefore, refer to these objects as very
high-redshift EROs (Z-EROS, herein). Methods. We analyze 63,550 galaxies
selected in the XMM-LSS field. To obtain a reasonably sized sample of EROs, it
is essential to consider a very wide area surveys. We identify targets within
an area of 0.77 square degrees for which optical to mid-infrared data are
available from SUBARU, UKIDSS, and Spitzer. We select Z-EROs based on their
colors, and then perform a selection of only OGs. One of our novel innovations
is to adapt the traditional method of EROs selection based on the filters I and
K, to higher redshifts. Using our method, we identify 20 objects that satisfy
the conditions required to be Z-EROs/OGs at redshifts 2.5<z<3.8 within some
conservative constraints of errors in the photometric redshifts. For each of
these objects, we calculate the corresponding color at rest (B-V), and estimate
their average stellar mass and age by comparing this color with a synthesis
model. Results. Our selected galaxies have high stellar masses (~10^{11} M_sun)
and are older than 1 Gyr, hence their stellar populations were formed at
z>~4.7. After including additional galaxies with z<2.5 analyzed in a previous
paper, we find that the formation epoch depends significantly on the observed
redshift and stellar mass: the higher the stellar mass, the lower the age of
the Universe at which it was formed. This result appears to conflict with
Lambda-CDM models that claim that the most massive galaxies formed after lower
mass.
