I checked out https://www.elastic.co/guide/en/elasticsearch/reference/current/_installation.html but I didn't see any OS requirements.
On that page it states, "The repositories do not work with older rpm based distributions that still use RPM v3, like CentOS5."
Bummer, I guess you will just need to use the tar.gz download then. It's OS agnostic.
"Elasticsearch requires at least Java 7."
Java 7 requires "Red Hat Enterprise Linux 5.5+" and above.
"CentOS version numbers ... correspond to the major version and update set of Red Hat Enterprise Linux (RHEL) used to build a particular CentOS release."
∴Elasticsearch requires CentOS version 5.5+, and will not function on CentOS 5.11.
That's what I was looking for. Thank you for inspiring me to track it down.