35 17 * * 5-7 sync; /sbin/shutdown -h +3 "server shutting down by cron job in 3 minutes time ..."
I think what centos82 is alluding to is that you need to be root or a some other user specifically authorized to execute the shutdown command. Your cron job may be working fine but the shutdown command would be erroring out if the user doesn't have the authority to perform a shutdown. You should
have received an email from the cron daemon that would show if any errors occurred.
And I just have
to ask: If you're shutting the system down for the weekend (presumably on Friday, i.e. day "5") why would you need to specify Saturday and Sunday.