Arduino, power supply and all servo grounds must be commoned. And of the course the servo signal wires will need to be connected to digital pins.
Whether 5V 5A will be enough for the power supply will depend on exactly what servos you use and how many of them. With no idea of what sort of project you're talking about no-one can be more definite. I know of servos that need more power than that for a single servo but they're not very common.
Steve