IMHO the issue is not "low power" but "slow". The time constant of 5 minutes is hard(ly) to realize by a pure analog circuit. Most likely a multistage counter will be needed, too. 75HC4060 can devide by 16k so 20ms ticks will do... It will draw around 8 uA.
An Ultra Low Power micro controller as the MSP430 uses 0.7uA in standby!
Atmels picoPower variants @1.8 V use the same 650nA in "power save mode", so the datasheet says. And yes, they are Arduinos!