A few suggestions:

Once you have fetched the page you could simply and blindly write it over the old version to the disk. That would be cheaper than calculating a checksum, esp. because you have to download the page twice (your function does not return the fetched data). So i would at least alter your code.

return ($md5, \$response);
[download]

Also, you do not return (but warn) when when the fetch fails. I didn't check what happens when you md5_hexing an undef value and what the code returns. It should return undef to indicate the failure to the caller. So, even if your code works, it would be simply clearer when you explicitly return undef when the fetch fails.

unless ($response->is_success)
{
  warn "Error while getting ", $response->request->uri,
       " -- ", $response->status_line, "\nAborting";
  return;
}
[download]