The backlight probably consists of several strings of leds. There are probably 2-3 leds in each series, and probably a couple of strings in parallel to light the screen. Each string consumes a certain amout of current. Typical leds range from about 20mA all the way up to 150mA and higher in some cases. For example, let's say you had a series of 2 leds with a 2.1V drop on each led. This would give you 4.2V drop for the series. If these leds took 50mA and you had 4 strings total, that would make 200mA. (just for example)
To determine the correct resistor value, just do the math as ericgibbs said.
You are supplying 5 volts. You know the forward voltage is 4.2V, and the current is 260mA. This leaves 0.8 volts to be dissipated on the resistor. R=V/I, so R = 0.8V/.260mA = 3.076 ohms (just repeating you ericgibbs)
Also important to keep in mind is the power of the resistor. In this case, the power the resistor will have to dissipate is 0.8V * 0.260mA = 0.208 watts.
Using a 1/4 watt resistor should be fine, but I would use a 1/2 watter to be safe.
//edit - sorry eric did not see your post