Each MAX7219 only turns on 8 LEDs at a time, so 160mA/MAX7219, so even 3 from an Arduino powered from 7.5V at the barrel to 5V from the regulator would be okay. That'd be 480mA, + 50 or so for the Arduino.
Here are 4 for example, running from 7.5V at the barrel jack. Not sure it's set for 20mA, had 10K resistors for Iset.
https://www.youtube.com/watch?v=hwYqgyMc5S4
(forum seems to add some extra characters to the start and end of links)
You can try putting a diode on the Arduino from 5V (anode) back to Vin (cathode) so the regulator is not reverse driven, some regulators are sensitive to that.