My general impression is that "simple" robotics is not very stressful in terms of the computing power required. Physical motion in the real world is pretty "slow" compared to the instruction speed of modern microcontrollers (even the slow ones.)
However, a lot of Arduino code is not very good at "doing 5 things at once", and simultaneous control of 5 motors, presumably with acceleration profiles and need for coordination to achieve particular paths means that you'll need to be careful (and one way to be careful is to have extra CPU power available.)
There ARE many 4-motor 3d printers based on slow AVR processors; you might want to check some of the printer forums to see to what degree CPU power has "limited" their abilities. (if you want to move much faster than a 3d printer head, you might need a faster CPU. And more expensive motors...)