A simple loop is all you should need. I believe this will work, but it's untested.
Code:
#!/bin/bash
filename="1234"
filelist="url1 url2 url3 url4 url5"
for i in $filelist; do
wget "${i}/${filename}"
done
Of course there are also a variety of download managers out there also. Probably some of them have the ability to do similar things. Try an apt-cache search or two.