Those are legal, at least in the EU. It's called "push support" or "walk assist", my bike engages it when I long-press the down button. It's purpose is to help you push the heavy e-bike up ramps and hills, but I mainly use it as a throttle when I ride behind my toddler on his balance bike.

It's closer to 3mph than 5mph, and as such needs some slow-riding skills, but it works.