Calculating the voltage drop of two Zener diodes in series? (reverse conducting)
If you really need to save power, you must use switching mode power regulator. Everything else will burn current, with passive dividers, Zener parametric stabilizers, or LDO regulators. 

To get optimal design, my advice is to go to TI.com, enter your design parameters (DC 6V-13V Vin, 5V 0.02A out), and launch their free WEBBENCH Power Designer. Here is the top of their 162 variants that meet your parameters:

 

If you don't want to mess with 7 components and inductor, here is a single-piece design using their module with integrated inductor:



But the latter is more expensive. Both designs will fit into 7x7mm area.

You might want to consider alternatives as LTC3642 ot ADP2360, they need only one inductor. I am sure there are many other options depending on market locality.