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Here's what I've tried so far:
- Made the default "ASP.NET Core API" project (the weather forecasting one) in Visual Studio
- Built it and copied the contents of the build folder to C:\Users\[My username]\TestService
- Ran the TestService executable. It says "Now listening on: http://localhost:5000"
- Open my browser, enter the "http://localhost:5000" URL. I get a 404 error. This is all on the same computer.
- Noticed that, under launchSettings.json, there were some other URLs listed, none of them localhost:5000. It gives 2 https URLs: https://localhost:7079 and http://localhost:5222. Both of these give "connection refused" errors.
- At this point, I don't know what else to do
Please help I don't want to lose my job
EDIT: I was able to figure out what was going on. Solution is here. Thanks to hypercracker and everyone else who advised 
Amber.