The rate doesn't actually matter. Over time and with a large pool of users it all averages out. Whether you charge fast or slow, your EV still consumes the same number of watts per day/week/month to cover your driving. (5A is about 600 watts, which is like having a space heater running: Not a small load.)

The wattage matters a great deal to the grid! If a whole neighborhood charges at max speed, that can become a problem. Here in Norway, you can get a discount on your electric bill if you let the grid operator adjust the charging speed at peak hours to help them balance load, and I guess frequency. A sensible approach.

600W is not much, that is an average gaming computer running a somewhat demanding game. Nerds all over the world have this as a multi hour nightly ritual. I choose to charge my car now and then instead :P