Electrical circuit / transformer in series?
Possible problems? Like it's a big old fire hazard, or won't work?

Don't connect anything in series with a 240 V load that isn't a power switch. It doesn't work like you think it does.

What you need is a transformer that connects in parallel to the 240 V, preferably by plugging it into its own outlet, and steps that down to around 6-9 V, which you can rectify, filter, and regulate down to 5 V. Which is what pretty much what an off-the-shelf 5 V wall wart does right now... so you may as well buy one of those.