While TrinityCore does not officially support MySQL version >= 5.6, there is a way to get it up and running.
You have to remove ONLY_FULL_GROUP_BY flag from MySQL's sql_mode variable in the MySQL config file so that all queries can be prepared correctly. (Certain queries used in the core are not compliant to this restriction and need to be rewritten in order to work. Hint: pull request )
If you're unsure how to do this please consult the MySQL documentation on http://search.oracle.com/search/search?q=sql+mode&group=MySQL