Voltage across inductor immediately after the switch is closed
No because at t = 0, there is no current flowing through the inductor but there is a current flowing through both resistors. 

Hence at t = 0 you have a voltage divider VL = 3/(3+2) * 5V = 3V

Extra credit: if the switch is closed for a long time, the voltage accross the inductor is 0. Hence no current is flowing through the 3kOhm resistor, and the current flowing through the inductor is 5/2k = 2.5mA.
The switch is opened: the current flowing through the inductor is still 2.5mA. Because the switch is open, this is also the current flowing through the 3kOhm resistor. Hence the voltage accross the inductor is -(3k*2.5mA) = -7.5V.