It would be easiest to get a precise output by just using an LDO, low dropout regulator. An old/common choice would be an LM1084.
http://www.ti.com/lit/ds/symlink/lm1084.pdf
It has a typical minimum load of 5mA and max of 10mA, so if it isn't stable at your 5mA load you might want to put a resistor between positive output and ground to give it 5mA more load, 10mA total... in this case the loss is negligible unless the device needs to run days at a time from small batteries.
http://www.ti.com/lit/ds/symlink/lm1084.pdf
It has a typical minimum load of 5mA and max of 10mA, so if it isn't stable at your 5mA load you might want to put a resistor between positive output and ground to give it 5mA more load, 10mA total... in this case the loss is negligible unless the device needs to run days at a time from small batteries.
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