> I don't know the current drawn by the backlight, only that
> the datasheet says to use a 5.1-ohm resistor from 5V.  I've
> determined that the proper brightness I need is 10 ohms at
> night, and 5 ohms during the daytime

Changing the value aside, if this is the current limiting resistor
how much current is it passing ? Typical forward voltage for a
backlighting LED array is 4.1V, leaving the R with 1V across it,
implying ~ 200mA / 200mW. Too much for CdS, even it were
the right resistance. I don't think you're going to get anywhere
with simple light sensors. Knowing the actual current the LEDs
are using would help

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