How can I make an LED glow by touching it with my finger?
If the situation was exactly like you sketched, then it cannot be explained that the LED lights up !

So something else is going on

Your power supply of 5 V is also capacitively coupled to the mains voltage and this causes a voltage between you and the 5 V supply.

All power supplies have this capacitive coupling caused by the transformer inside it and a small value capacitor between mains and output to prevent emissions of high frequency signals. The total capacitance will usually be less than 1 nF but that is enough to light up a sensitive LED.

Try this again with a battery and you'll see the LED does not light up.