The cord was just used to tie the adapter to the plug/electrical cord to keep it from getting lost.
You could then just ignore the adapter and insert the plug straight into a wall outlet, or couple it up to the adapter and plug into a lighting pendant from the ceiling.
On that 5A plug, I remember having a lot of those around at my grandparents' house in the the 1970s. I'm not sure when the design first appeared, but I think they were probably still being made in the 1940s.
