The backlight part of the screen is a led panel. I think that the maximum supported illumination is provided when you apply the power on backlight pins (unless some hardware guru from forums prove we wrong)
Usually there are chip resistors built onto the display PCB so that you get the correct maximum current with a 5V supply. You would normally add extra resistors (or use PWM) to reduce the brightness.
If you apply more than 5V the LEDs will glow brighter, but you will probably damage the display because of the extra heat this will generate. Most displays I have seen are fairly bright, unless you want to view them in full daylight... but then you don't really need the backlight for illumination anyway.