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.