  The discovery of galaxies with regularly rotating discs at redshifts $\geq$
has been a puzzling challenge to galaxy formation models that tend to predict
chaotic gas kinematics in the early Universe as a consequence of gas accretion,
mergers and efficient feedback. In this work, we investigated the kinematics of
five highly resolved galaxies at z $\sim$ 4.5 observed with ALMA in the [CII]
158 $\mu$m emission line. The sample is diverse: AzTEC1 (starburst galaxy),
BRI1335-0417 (starburst and quasar host galaxy), J081740 (normal star-forming
galaxy) and SGP38326 (two starburst galaxies in a group). The five galaxies
show velocity gradients, but four were found to be rotating discs while the
remaining, AzTEC1, is likely a merger. We studied the gas kinematics of the
discs using 3DBAROLO and found that they rotate with maximum rotation
velocities between 198 and 562 km/s while the gas velocity dispersions,
averaged across the discs, are between 49 and 75 km/s. The rotation curves are
generally flat and the galaxies have ratios of ordered-to-random motion
(V/$\sigma$) between 2.7 and 9.8. We present CANNUBI, an algorithm for fitting
the disc geometry of rotating discs in 3D emission-line observations prior to
modelling the kinematics, with which we find indications that these discs may
have thicknesses of the order of 1 kpc. This study shows that early disc
formation with a clear dominance of rotation with respect to turbulent motions
is present across a variety of galaxy types.
