Ok, the user's crontab is working. Now about the permissions: the script should be executable by the user (but you can always change the ownership of the script). The file instead cannot by removed by a normal user, not only because permissions prevent it:
-rw-r--r-- 1 root root 17383315 2013-01-30 09:51 dklog.log
but also because the directory where the script is placed should belong to (or have permissions for) the crontab owner. And maybe for this reason the log file placed in the same directory has not been updated by the date command in your script. What about trying something like this, just for testing purposes?
*/5 * * * * /opt/scripts/dklogremv.sh > $HOME/cron.log 2> $HOME/cron.err