How to zero pad a sequence of integers in bash so that all have the same width?

Easier still you can just do

for i in {00001..99999}; do
  echo $i
done

use printf with "%05d" e.g.

printf "%05d" 1

In your specific case though it's probably easiest to use the -f flag to seq to get it to format the numbers as it outputs the list. For example:

for i in $(seq -f "%05g" 10 15)
do
  echo $i
done

will produce the following output:

00010
00011
00012
00013
00014
00015

More generally, bash has printf as a built-in so you can pad output with zeroes as follows:

$ i=99
$ printf "%05d\n" $i
00099

You can use the -v flag to store the output in another variable:

$ i=99
$ printf -v j "%05d" $i
$ echo $j
00099

Notice that printf supports a slightly different format to seq so you need to use %05d instead of %05g.

If the end of sequence has maximal length of padding (for example, if you want 5 digits and command is seq 1 10000), than you can use -w flag for seq - it adds padding itself.

seq -w 1 10

would produce

01
02
03
04
05
06
07
08
09
10