A zener diode versus a linear regulator for a 5 V 100 mA output
Placing a single 5V1 zener diode with a resistor is not a good idea. 

Zener-Transistor Regulator: Consists of a 5V6 zener (500mW or even smaller), a BD- series NPN transistor (e.g. BD241 or BCP56), 1 or 2 resistor and 2 electrolytic and 2 ceramic caps. 

L7805 or AMS1117-5 Linear Regulator: Should be TO-220 or D²PAK package. Don't even try TO-92. Of course you need at least 2 electrolytic and 2 ceramic (100n or so) caps.

In either ways, the power dissipation of the regulator element (power transistor in opt.1, L7805 or AMS1117-5 on opt.2) will be at least 
$$
Pt = (Vs - Vo)  Io = (12 - 5) 0.11 = 770mW. 
$$
For a TO-220 package, Rth = 62.5°C per Watt, hence the temperature rise of the regulator element will be 
$$
\Delta T = Rth * Pt = 62.5 * 0.77 = 48°C
$$
And if we suppose the ambient temperature is about 24°C, the temperature of the regulator will be 72°C! You do need a heatsink (with black anodized coating recommended).

Why don't you try a simple cellphone charger?