  Over the past two decades, our knowledge of the high-redshift (z > 5) radio
quasars has expanded, thanks to dedicated high-resolution very long baseline
interferometry (VLBI) observations. Distant quasars provide unique information
about the formation and evolution of the first galaxies and supermassive black
holes in the Universe. Powerful relativistic jets are likely to have played an
essential role in these processes. However, the sample of VLBI-observed radio
quasars is still too small to allow meaningful statistical conclusions. We
extend the list of the VLBI observed radio quasars to investigate how the
source structure and physical parameters are related to radio loudness. We
assembled a sample of 10 faint radio quasars located at 5 < z < 6 with their
radio-loudness indices spanning between 0.9-76. We observed the selected
targets with the European VLBI Network (EVN) at 1.7 GHz. The
milliarcsecond-scale resolution of VLBI at this frequency allows us to probe
the compact innermost parts of radio-emitting relativistic jets. In addition to
the single-band VLBI observations, we collected single-dish and low-resolution
radio interferometric data to investigate the spectral properties and
variability of our sources. The detection rate of this high-redshift,
low-flux-density sample is 90%, with only one target (J0306+1853) remaining
undetected. The other 9 sources appear core-dominated and show a single, faint
and compact radio core on this angular scale. The derived radio powers are
typical of FRII radio galaxies and quasars. By extending our sample with other
VLBI-detected z > 5 sources from the literature, we found that the core
brightness temperatures and monochromatic radio powers tend to increase with
radio loudness.
