Do you want to compare the five last characters from column "Address3" with column "ZIP" and you want all lines where these a different?
Assuming that column "ZIP" is a text or varchar column.
In the examlpe below you have to replace "Your_Table_Name" with the right table name of course.
WHERE substr(Address3,length(Address3)-4,5) <> ZIP;
See also the related functions in the official PostgreSQL documentation:
PostgreSQL: Documentation: 9.1: String Functions and Operators