You would be better off using rename (prename on some systems) since that allows you to use Perl regular expressions to do the renaming, along the lines of:
prename 's/^.{5}//' *.nai
The reason your script is not behaving is that, for every source file, you're attempting to rename it to every target file.
If you need to limit yourself to using that script, you need to work out the single target file for each source file, something like:
#!/bin/bash
for i in *.nai; do
y=$(echo "$i" | cut -c6-)
mv "$i" "$y"
done
