Supermassive black holes are growing slowly by z∼5

We investigate the black hole mass function at z similar to 5 using XQz5, our recent sample of the most luminous quasars between the redshifts 4.5 < z < 5.3. We include 72 quasars with black hole masses estimated from velocity-broadened emission-line measurements and single-epoch virial prescriptions in the footprint of a highly complete parent survey. The sample mean Eddington ratio and standard deviation is log lambda approximate to -0.20 +/- 0.24. The completeness-corrected mass function is modelled as a double power law, and we constrain its evolution across redshift assuming accretion-dominated mass growth. We estimate the evolution of the mass function from z = 5-4, presenting joint constraints on accretion properties through a measured dimensionless e-folding parameter, k(ef) equivalent to <lambda > U(1 - & varepsilon;)/& varepsilon; = 1.79 +/- 0.06, where <lambda > is the mean Eddington ratio, U is the duty cycle, and & varepsilon; is the radiative efficiency. If these supermassive black holes were to form from seeds smaller than 10(8)M(circle dot), the growth rate must have been considerably faster at z >> 5 than observed from z = 5-4. A growth rate exceeding 3 x the observed rate would reduce the initial heavy seed mass to 10(5-6)M(circle dot), aligning with supermassive star and/or direct collapse seed masses. Stellar mass (10(2)M(circle dot)) black hole seeds would require greater than or similar to 4.5 x the observed growth rate at z >> 5 to reproduce the measured active black hole mass function. A possible pathway to produce the most extreme quasars is radiatively inefficient accretion flow, suggesting black holes with low angular momentum or photon trapping in supercritically accreting thick discs.