  Galaxies at high redshift with a strong Ly-Alpha emission line trace massive
star formation in the absence of dust, and can therefore be regarded as a prime
signature of the first major starburst in galaxies. We report results of the
Ly-Alpha search within the Calar Alto Deep Imaging Survey (CADIS). With imaging
Fabry-Perot interferometer CADIS can detect emission lines in three waveband
windows free of night-sky emission lines at 700nm, 820nm, and 920nm. The
typical flux detection limit for Ly-Alpha emission redshifted into these
windows, Flim > 3X10^(-20) Wm^(-2), corresponds to (unobscured) star formation
rates of >10Msun/yr at z=6. Candidate Ly-Alpha-emitting galaxies are selected
from the total emission line sample, which contains more than 97% of objects at
z<1.2, by the absence of flux below the Lyman limit (B-band "dropouts"), and
the non-detection of secondary emission lines in narrow band filters. We have
detected 5 bright Ly-Alpha-emitting galaxy candidates at z ~ 4.8, and 11
candidates at z ~ 5.7. For two of four observed Ly-Alpha candidates, one
candidate at z ~ 4.8, and the other at z ~ 5.7, the emission line detected with
the Fabry-Perot has been verified spectroscopically at the VLT. When compared
to Ly-Alpha surveys at z<3.5 even the upper limits set by our list of
candidates show that bright Ly-Alpha galaxies are significantly rarer at z>5
than the assumption of a non-evolving population would predict. Therefore we
conclude that the Ly-Alpha bright phase of primeval star formation episodes
reached its peak at redshifts between 3 and 6.
