We bought the ESC blue-boat variant Basic ESC 500, and there are two small cables, black and red. Per the documentation, they are the BEC cables, but I need help understanding what I should connect there. Or is it a power supply of 5V?
The BEC is a regulated 5V output from the ESC that can be used for powering other electronics. If you don’t require a 5V supply then you can leave those wires disconnected, although for safety you likely want to cover the exposed conductors with some electrical tape.
In case it’s relevant, the Basic ESC 500 product page specifies that
so be aware that any external electronics you connect to it are limited to 5A of current draw.