Using only bash, you could do this:
for file in *nai* ; do
echo mv -- "$file" "${file:5}"
done
(Remove the echo
when satisfied with the output.)
Avoid ls in scripts, except for displaying information. Use plain globbing instead.
See also How do I do string manipulations in bash? for more string manipulation techniques.
Your script can't work with that structure: if you have 5 files, it will call mv
five times for the first file (once for each element in the second list), five times for the second, etc. You'd need to iterate over the two sets of names in lockstep. (It also doesn't deal with things like whitespace in filenames.)