What's the simplest 110ac to 5vdc circuit that can power an ESP wifi board?
Well you did ask whats the simplest circuit so...







simulate this circuit &ndash; Schematic created using CircuitLab

You might prefer to just use an old 5V cellphone charger. This would be easier, and poses less risk of electrocution. On the subject of safety, the pcb layout pictured on Aliexpress appears to have insufficient clearance around the relay for mains voltages.

Now since the nervous nellies are getting their knickers in a twist about it being directly connected to the mains, and therefore dangerous. 
They seem to have failed to notice that 


this is a completely legal design, from the electrical safety point of view, as you are using a wireless device, and while it is in a box, it is safe. 
the power supply is no more dangerous that the wires and PCB connections to the switching relay when switching mains.
when working with "hot" circuits use an ELCB/GFCI 




That said, while this is the simplest power supply (what you asked for), it is very inefficient, gets hot, and has the main safety concern - you can break the glass bulb. It would however be perfect for an IOT egg incubator, or dry cabinet, but not much else.



How to make a transformerless supply for some of these low cost wireless devices is a pretty interesting question. The usual trick is a series capacitor, but the capacitor gets big and expensive for higher currents, like those needed to operate a 5V coil relay (e.g. 80mA).

This trick uses a higher coil voltage (24V=lower current 16mA), and puts the relay in series with the 5V supply, so it doesn't increase the current when on at all.







simulate this circuit

Now if you touch the output and phase and neutral are swapped, a fatal shock is possible. But if we split the capacitor, then the current is limited regardless of which wire is phase. A 30mA shock in unlikely to kill, so this arrangement can be much less likely to be lethal. In fact you will observe that on 120V, the voltage will only be 60V, which the IEC considers "safe to touch with dry hands"







simulate this circuit

If we were using something much lower power than a relay, then if we used Type Y2 safety capacitors, and have current less than 3.5mA, which would run a bluetooth device for example, then it would be considered safe under IEC950 (according to this)