I did not know the */5 syntax, but tried it, and it works.
There is still the issue with "root" mentioned on every line, and I'm sure this won't work.
Also, why do you mention the SHELL and PATH variables???
Please remove this from the crontab entries
Here is what I suggest you put in your cron (using crontab -e)
<quote>
5 * * * * echo "****************"|mail -s "eeeee"
abc@gmail.com
55 * * * * cd / && run-parts --report /etc/cron.hourly
*/1 * * * * echo cron-works>/tmp/cron-works.txt
</quote>
you should see a file created in /tmp every minute (check with ls -l)