  We present observations with the IRAM Plateau de Bure Interferometer of three
QSOs at z>5 aimed at detecting molecular gas in their host galaxies as traced
by CO transitions. CO (5-4) is detected in SDSSJ033829.31+002156.3 at z=5.0267,
placing it amongst the most distant sources detected in CO. The CO emission is
unresolved with a beam size of ~1", implying that the molecular gas is
contained within a compact region, less than ~3kpc in radius. We infer an upper
limit on the dynamical mass of the CO emitting region of ~3x10^10
Msun/sin(i)^2. The comparison with the Black Hole mass inferred from near-IR
data suggests that the BH-to-bulge mass ratio in this galaxy is significantly
higher than in local galaxies. From the CO luminosity we infer a mass reservoir
of molecular gas as high as M(H2)=2.4x10^10 Msun, implying that the molecular
gas accounts for a significant fraction of the dynamical mass. When compared to
the star formation rate derived from the far-IR luminosity, we infer a very
short gas exhaustion timescale (~10^7 yrs), comparable to the dynamical
timescale. CO is not detected in the other two QSOs (SDSSJ083643.85+005453.3
and SDSSJ163033.90+401209.6) and upper limits are given for their molecular gas
content. When combined with CO observations of other type 1 AGNs, spanning a
wide redshift range (0<z<6.4), we find that the host galaxy CO luminosity
(hence molecular gas content) and the AGN optical luminosity (hence BH
accretion rate) are correlated, but the relation is not linear: L(CO) ~
[lambda*L_lambda(4400A)]^0.72. Moreover, at high redshifts (and especially at
z>5) the CO luminosity appears to saturate. We discuss the implications of
these findings in terms of black hole-galaxy co-evolution.
