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After Updating my Xperia Z to Anroid 5.0, the external speker does not work when playing media such as music and videos. It works however, when I receive notifications from applications and alarms. Before updating it was fine though.
I suggest that you try to repair the phone software using PC Companion..
Before repairing your device you may want to backup your information first. Check out this topic for more information on how to.
How to backup?
If the issue should still remain I think that this needs to be examined and fixed at a repair center. For more information about how to submit your phone for repair and where, contact your local support team.