How to make an LED turn on if the input voltage is below 5V?
To make a 5 V low voltage detector I'd try this circuit:

I found that here.
Changes you need to make:
There are 2 LEDs in series, I would use only one LED, so leave out LED2 (so connect the bottom side (cathode) of LED1 directly to -Battery (= ground).
To make the LED burn brighter, I make R1 = 1 kohm (instead of 2.2 kOhm).
R3 needs a different value, use 5.3 kOhm, that's not a standard value so use two resistors in series: 4.7 kOhm + 680 Ohms.
With that the LED should turn on when the (Battery) voltage drops below ~4.7 V.
With those changes, the end result is this circuit:



simulate this circuit &ndash; Schematic created using CircuitLab
(Yes, that TL431 is the symbol of a Thyristor, I know, I was too lazy to draw a proper symbol ;-) )
I didn't try this circuit but I'm quite sure it will do the job.