Well, let's see. Aside from (as already noted) the President can't do that?
• Let's start with a key fact:
Southern border crossings are significantly down since 2000.
That wasn't due to enforcement, by the way. It's mostly because Mexico's economy improved.
I.e. you can either scream about Mexicans "stealing our jobs!" (by those jobs moving to Mexico, which improves Mexico's economy) or you can scream about Mexicans "stealing our jobs!" (as a result of higher immigration, due to poor economic prospects in Mexico). Sorry, you can't have both. Moving on....
• Another key fact: Physical walls don't stop anyone, that's a fantasy. In fact, if your goal is to reduce the permanent migrant population, they backfire. When people can cross the border easily, they spend a few months in the US to work (usually in agriculture) then go home, because the costs involved are low. The tougher it is to cross, the greater the incentive to stay in the US.
• Another key fact: $5 billion will barely build anything resembling a wall along the border. Seriously. Just think about basic cost overruns and delays on any big infrastructure project, then delay it by 10 years as the government faces a barrage of lawsuits over environmental impacts and eminent domain. We'd be lucky if it only cost $70 billion.
• Most undocumented immigrants now are coming from Asia. They fly to the US, and overstay their visa. Walls don't help with that one.
• Like it or not, asylum is a human right that is part of US law -- and that is not likely to change any time soon. Even if we spend $70 billion on a massive wall, even if it somehow works, it's going to wind up creating a massive human rights crisis on the border, that Mexico will not want to pay for. And hey! Already there. Wanna bet it won't stop next year's caravans?
Sounds to me like if you really don't want brown people crossing the southern border, the best policy is to improve their lives in their home nations, so they have less incentive to migrate.