Steps to reproduce:

1. Install Zabbix from RPMs at http://repo.zabbix.com/zabbix/5.0/rhel/7/x86_64/
2. Make any required changes to be able to start zabbix-server.service
3. systemctl start zabbix-server.service

Result:
The server starts, but only after logging an error in the journal for the service:

Dec 28 10:15:47 server.interlinx.bc.ca systemd[1]: Starting Zabbix Server...
Dec 28 10:15:48 server.interlinx.bc.ca systemd[1]: Can't open PID file /run/zabbix/zabbix_server.pid (yet?) after start: No such file or directory
Dec 28 10:15:48 server.interlinx.bc.ca systemd[1]: Started Zabbix Server.

Expected:
Should start without the Can't open PID file /run/zabbix/zabbix_server.pid (yet?) after start: No such file or directory error.

This would seem to be a problem of zabbix-server perhaps taking too long to create the PID file so that systemd cannot find it when zabbix-server has dæmonized and exited it's parent process.