Basically Dave, no such thing as a 5v red LED.
Different colours drop different voltages across them when operating due to the semiconductor materials used; e.g. red are usually 1.8v to 2v; green around 2.2v, blue somewhat higher.
The normal way of driving an LED is from a constant voltage via a resistor; the voltage drop in the LED will give the voltage across the resistor and therefore the current through the pair (e.g. a 5v supply to a red LED will drop 3v across the resistor, so a current of 1mA on a 3k resistor, 10ma on 300 ohm etc (V = IR; I = V/R))
So if there is nothing hanging on the back of the existing LED it is most likely a standard (i.e. cheap) led with a resistor on the circuit board feeding it. I'd be looking at something like this: https://www.ebay.co.uk/itm/152508668100
though they're expensive to a tight git like me - I just bought a couple of hundred for a project (surface mount, though) at 0.7c each
The LEDs you see advertised as '12v' include either an inline resistor or a constant current chip, but unless your existing LED has something hidden in it (or in heat shrink close to the LED) then it's most likely just a standard beastie.
Beware: they are polarity conscious; wired the wrong way around probably won't hurt them, particularly if there's a series resistor, but they won't light up. That style normally has one lead longer than the other and *may* have a flat on the case; observe the original.