Despite considerable observational efforts in recent years, it is still not clear when was the epoch of fast growth for most super massive black holes (BHs), which reside in the centers of most galaxies. Such an epoch is expected both from theoretical models and the observed masses of BHs in the local Universe. We present new H-band spectroscopy for a flux limited sample of 40 z~4.8 active galactic nuclei, selected from the Sloan Digital Sky Survey. The spectra were obtained with the Gemini North (NIRI) and the VLT (SINFONI) observatories. The sample probably contains the most massive active BHs at this redshift and spans a broad range in bolometric luminosity, 2.7x10⁴⁶< 2.4x10⁴⁷ erg/sec. The high-quality observations and the accurate fitting of the MgII(2800A) line, enable us to study, systematically, the distribution of BH mass (M_BH) and normalized accretion rate (L/L_Edd) at z~4.8. We find that 10⁸ < M_BH < 6.6x10⁹ M_sun, with a median of ~8.4x10⁸ M_sun, and also that 0.2 < L/L_Edd < 3.9 with a median of ~0.6. Most of these sources had enough time to grow to their observed mass at z~4.8 from z=20, assuming a range of seed BH masses, with ~40% that are small enough to be stellar remnants. Compared to previously studied samples at z~2.4 and 3.3, the masses of the z~4.8 BHs are typically lower by ~0.5 dex. and their L/L_Edd is higher by a similar factor. The new z~4.8 sample can be considered as the progenitor population of the most massive BHs at z~2.4 and 3.3. Such an evolutionary interpretation requires that the growth of the BHs from z~4.8 to z~3.3 and then to z~2.4 proceeds with short duty cycles, of about 10-20%, depending on the particular growth scenario.