I have an Oracle XE 11g instance that I've just patched from 5.1.0 to 5.1.4
I ran @apxpatch.sql, then copied over the images folder.
select * from v$version
Oracle Database 11g Express Edition Release 11.2.0.2.0 - 64bit Production
select * from apex_release
5.1.4.00.08
2016.08.24
APPLIED
Now when attempting to navigate to the application builder, I see this error

Error during rendering of region "Application Express - Sign In".
ORA-06508: PL/SQL: could not find program unit being called
The only thing I haven't done is restart the tomcat server, since I'm not sure how on this particular EC2 instance.
I found no errors in the apxpatch.log, and clean commentary at the start/end.
Googling this particular error doesn't reveal much. I'm not sure what I may have missed, I don't involve myself much in this facet of APEX.
Cheers,
Scott