The datasheet states a base:collector current of 1:250 for a TIP120 darlington used as a switch (Figure2, page3).
With 5volt drive, and 1.5volt BE drop, there is ~3.5volt across the base resistor.
Base current needed is 1.1A (solenoid) / 250 = 0.0044A = 4.4mA.
Theoretical base resistor value = 3.5volt / 0.0044Amp = 795ohm.
Practically, anything between 220ohm and 1k will do.
Don't forget the kickback diode across the solenoid.
Not having one could kill the transistor.
Leo..