I get a couple of errors, the first one the patch fails on the first hunk for app/code/core/Mage/Core/Model/Email/Template/Filter.php
The second error is it can't find the file app/code/core/Zend/Xml/Security.php On closer examination, I don't even have an app/code/core/Zend/Xml directory in my installation!
I don't see any prerequisite patches listed for SUPEE-7405, is there?