Rb = (5 - 0.8)/22.85 = 184 ohms
That should be: Rb = (5 - 0.8)/0.02285 = 184 Ohms
Once the transistor is fully on the base current beyond that isn't critical so I would go for 30 mA which is still well within the 40 mA maximum for the Arduino pin. That would calculate out as 140 Ohms.
- I am aware that LEDs in parallel need to have a resistor for every LED. Is it possible to use a single resistor at the anode of every led instead of wiring 3 per LED.
No. Current is the quantity of electrons. For components in series the current is the same through each component. For components in parallel the current is shared across the components. If you use a single resistor for three LEDs the current through the resistor has to be the SUM of the current through each LED. Unfortunately there is no way to force that current to be shared equally across the three LEDs. You end up with some LEDs hogging the current and burning out.
If you had separate LEDs instead of RGB units you could put LEDs of the same color in series and use a higher voltage to drive them. If they are in series they all get the same current. A constant-current driver or single resistor can then adjust current for all of them. Twenty in series would require 20 to 60 volts so usually parallel and series are combined: Four strings of five, for example. Each 'string' needs a resistor or constant-current driver.