Flask's built-in server is not intended for production use - or at least, the documentation refers to it as a "local development server".
For production, something like Tornado, gunicorn, or even Apache is what you'll need to be using.
See also: Flask documentation covering the Flask.run()
method.
That said - it's just a Python program. There's no reason you couldn't run your own on a different port via app.run(port=5001)
.