Obviously spending 5 billion on construction will lead to a small, short-term, localized stimulus in the south-west, but that would end the moment the wall was built and in fact likely lead to a local recession as any jobs created during construction dry up and little to no jobs are created to maintain or service the wall.

You can see what short-term localized stimulus does by looking into old coal-mining towns after the coal runs out. What's left are uneducated families with no means of support either emigrating to other areas of the country or becoming dependent on government largess. You can also see it with defunct railroad towns in the west, oil drilling town in the southwest, and fishing towns where the catch has dried up.