Can I use a transistor as a relay?

I have a hardware component that requires 5V and 300mA to work. The Arduino output current of the Pins is 50mA, to the best of my knowledge. Only 40mA for 5V Pins.

My idea was to use the 5V and 2A of a phone charger, and switch it on using a relay and one of the IO pins. The relay is designed for 230V usage. Not sure if that would even work.

I thought of using a transistor, which is capable to handle that kind of voltage and current (TIP120). However, I am not sure how to connect the circuit around it, as the Collector and Emitter would be connected to the 5V 2A from the phone charger, but the Base would be connected to the Arduino, without the same ground. Anyone have ideas to design this? Thanks.