Nokia E5 Keypad Light LED Jumper Ways 
Troubleshooting hints for Nokia E5 not working keypad backlight LED problem:
1. Check a certain LED's that won't light up using a multimeter. The white LED bulb are connected in parallel. Replace if found damaged.
2. Trace each certain connection line paths for possible cut off or open circuit.
3. Check the 3.7v VBAT (battery voltage) across the inductor coil.
4. Check/replace the inductor coil.
5. Check/replace the diode.
6. The LED's negative supply voltage is feed from the GAZOO IC.
There is a possibilty if the GAZOO chip is faulty, it will result to keypad light problem.
Reworking it might only fix the problem or replace if necessary.