In a newly setup digitalOcean cloud server (CentOS), I have installed php and Apache. The webserver is running fine:
[root@a2m5cent01 httpd]# service httpd s
Since everything looks at its default state, have you checked this part just for confirmation
cat /etc/php.ini | grep log_errors
If log_errors is disabled then enable it and check this below log after restarting httpd.
/var/log/httpd/error_log
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Also check this part from php configuration.
cat /etc/php.ini | grep error_reporting
This value should be enabled by default so that display_errors will work.
error_reporting = E_ALL