Is there a v simple way to detect small mV & light an LED (1 transistor?)

[741]

I've made a board which supplies multiple Zinc Oxide gas sensors with 5V (they need a 48 hour burn-in according to the mfg).

It would be nice to shine an LED when a sensor is plugged in, but I have 5.0V rail already (the recommended value), and I do not want to drop more than say 10mV for sensing.

(Note: For now at least, I'm accepting the mfg strict guidelines of 5V (+/- 0.1V), even though I suspect it is not so critical, especially for this conditioning phase).

I'd like to avoid using say 1 op-amp per sensor, and I hope it is possible with maybe 1 transistor per sensor...

[Kleinstein]

Transistors have a typical temperature drift of some 2 mV/K for the base emitter voltage. So they are not really suitable to detect a drop if some 10 mV reliably in a simple circuit (it works with multiple transistors).
I would suggest using OPs / comparators (e.g. LM358 / LM393 or similar). These are relatively cheap and 2 in a 8 pin case. They can sense some 10 mV near ground level.

[Seekonk]

I've used a pair of TL431 as a current sense.  One is set to 2.5V as a reference and the common return is thru a shunt.  The other has its reference pin tied to the first one thru a small voltage divider on the other side of the shunt.  This one drives a LED. This will easily detect just a couple mv.