dc42:
On all the LCD displays I have used, the backlight LCD A and K wires are soldered on to the board at one end of the display. Use a multimeter to check the resistance between those joints and the backlight connections on the edge of the board. That way, you can tell whether there is already a resistor on the board.
Using a multimeter, I found out that there is no resistance. However, I traced the connections with my eyes and found a 47 ohm resistor. I thought this was good enough so I connected the backlight directly to +5v and it worked without burning out! Thanks for your help.