Voltage regulator circuit, efficient, low necessary drop
A zener diode is absolutely no good for very low power (for the 1N4732A the zener voltage is specified at 53mA), and even LDOs often have ground currents 10 times your 5\$\mu\$A load. You want an LDO with a &lt; 1\$\mu\$A ground current, like Seiko S-812C40. Output voltage is 2.0 to 6.0 V, selectable in 0.1 V steps, so there's also a 4V type. You get 65mA out. Dropout as low as 120mV, and stable even without output cap. The S-812C is available in SOT-23.  

edit
I just discovered that there's also a version with a shutdown. That S-812C is even cooler than I thought! :-)