one other possibility is that since wget is just triggering the /admin/cron.php,
you could use another trigger such as lynx, which may not be disabled.
In that case, try
*/5 0 * * * lynx -dump http://www.quoll.com > /dev/null 2>&1
Maybe your webhost doesn't see lynx as a threat (most scripts use wget because it was designed for scripting).
Let us know how you go