Spatially extended Ly-alpha sources that are faint and/or compact in coninuum are candidates for extremely young (~< 10^7 yrs) galaxies at high redshifts. We present medium-resolution (R~2000) spectroscopy of such extended Ly-alpha sources found in our previous study at z~3-5, using VLT/VIMOS. The deep spectroscopy showed that all 18 objects we observed have large equivalent widths (EWs) exceeding 100 A. For about 30% of our sample (five objects), we identified conspicuous asymmetry on the profiles of the Ly-alpha line. They show broad wing emission components on the red side, and sharp cut-off on the blue side of the Ly-alpha line. Such asymmetry is often seen in superwind galaxies known to date, and also consistent with a theoretical prediction of superwind activity. There are eight objects (8/18 ~ 40%) that have large EWs exceeding 200 A, and no clear signature of superwind activities. Such large EWs cannot be explained in terms of photo-ionization by a moderately old (>10^7 yrs) stellar population, even with a top-heavy IMF or an extremely low metallicity. These eight objects clearly show a positive correlation between the Ly-alpha luminosity and the velocity width. This suggests that these eight objects are good candidates for forming-galaxies in a gas-cooling phase.
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