I'd like to know which version of Java EE specification is provided by my Websphere application server (traditional, not Liberty). Unfortunately I don't know where to find such information. WAS version is
WebSphere Platform 8.5.5.11 [BASE 8.5.5.11 cf111649.01] [IBMJAVA8 8.0.3.20 cf111647.02]
Accordingly with IBM doc it should be version 6.
The complete list is here: https://www.ibm.com/support/knowledgecenter/en/SSAW57_8.5.5/com.ibm.websphere.nd.doc/ae/rovr_specs.html
<dependency>
<groupId>javax</groupId>
<artifactId>javaee-api</artifactId>
<version>6.0</version>
<scope>provided</scope>
</dependency>
The OP asked about WebSphere Application Server traditional base 8.5.5, the definitive answer is JEE6 as listed in this IBM KnowledgeCenter doc. WAS traditional v9 brings the spec level to EE7 as noted here. Liberty, as noted in this KnowledgeCenter doc, has supported JEE7 since version 8.5.5.6 . The Oracle doc referenced above verifies that WAS Liberty is JEE7 certified from 8.5.5.6 and that WAS traditional is from v9.
Your version is compliant with Java EE 7, and has been certified by Oracle. You can see that at http://www.oracle.com/technetwork/java/javaee/overview/compatibility-jsp-136984.html which lists all Java EE certified servers.