So you have Arduino sourcing current into the LED anodes, and sinking current for a layer 's cathodes via NPN transistor?
Vbe Saturation is 0.65V to 0.95V with Vce Sat of 0.2V to 0.3V with Ib base current of 1 to 5mA for Collector current of 10-50mA, see page 2 of the datasheet.
So picking some numbers in the middle, say Vbe 0.8V, Vce 0.3V, and Ib 5mA:
Then LED resistor: (5V - 3.2V - 0.8)/15mA = 67 ohm 68 is standard value
Base resistor: (5V - 0.3V)/5mA = 940 ohm. Want to make sure transistor turns on fully, so use a standard value of 910 ohm or 820.
(5-.3)/820 = 5.7mA