I would think 120 ohm would be fine.
As is, you have ~0.7V across the cathode transistor Vce, say 1.5V across the diode, and 0.7 across the anode transistor Vbe, plus whatever is developed across the transistors. So the anode transisitor base can't go lower then ~2.9V. (5V from arduino pin - 2.9V at anode transistor base)/120 = 17.5mA.
You could measure the voltage across your resistor, or put your multimeter in mA mode and put it series, and confirm.
Why would you want a 25V supply? You will just dissipate a lot of voltage across the resistors then. 5V is plenty. Take some measurements across your parts, 3.3V might be enough even.
As you've seen, the top transistors are not even needed - you can use the Arduino output to control the current out. Only 1 LED in each column is on at 1 time if you are multiplexing. You need the cathode transistors to sink the current from multiple LEDs being on in a row. Keep the resistor feeding the anode, ditch the resistors on the cathodes.