Powering a 5V device directly from the wall socket is impossible without a 5V power supply that works as an AC to DC adaptor. With all USB devices running on 5 volts, mains to USB power supplies are very common. Similar power supplies with different connectors, such as barrel plugs, are also available. Most power supplies use British standard mains plug, but people who travel often might choose one with interchangeable plugs.
Car batteries can power 5V devices, but because they produce 12 volts DC, it's necessary to use a step-down DC to DC converter. For universal purposes, there is a selection of regulated switching power supplies that cover a wide range of voltages. With safety in mind, always look for a power supply that offers protection against overload, over-voltage, and short circuit.