Most backlight inverters are designed for 12VDC inputs. Some work with 5V, but I don't know of any that work with the range you need in your application (some publish 0-15V ranges, but brightness varies in proportion to the input voltage). Here are a couple solutions:
5V Backlight Inverters
If you use a DC-to-DC converter to power the backlight inverter, you could use any one of the following 5V backlight inverters (these would work for the 6.4-inch LQ64D343 display we currently use with our systems):
Taiyo Yuden (formerly Xentek) LS655; has different input connector than ADS boards
Linfinity LXM1622-05-01; uses 8-pin Molex input connector, different from ADS
ERG E1957: not dimmable
You can get datasheets for these at the manufacturer sites listed at this topic. If power consumption on your system is an issue, make sure that you use a very high efficiency converter.
12V Battery and Inverter
Another approach is to use a 12V battery. Many of the 12V inverters have a wider input voltage range (either 10 or 20% tolerance) than the 5V inverters (usually 5% input tolerance). This would allow direct connection to most 12V battery types.