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I am sure other people on here will shoot me down in flames but a 555 timer chip is suitable for this. You can set the ON and OFF periods using different resistors and capacitor values. The link below should point you in the right direction.
(Your output would be a relay that would switch on or off your pump circuit)
I think you can use a 556, dual timer IC, and configure each timer as a one-shot, each feeding the other's trigger input. Program one for the 20min off time, and the other for the 5 second on-time. I've never tried to program a timer for such a long time period, but I think it can be done, just be sure to use low-leakage capacitor types, such as tantalum.
Sorry, I don't have time to draw a schematic, but here is a good primer/turtoral.
Theoritically, it shoulnd't be that hard. One tantalum I looks at leaks .1ua at room temp. If you pair a 100ufd version of this cap with a 12 MΩ resistor, that gives you the 20 minute delay with only 12*.1 = 1.2 volts drop across the resistor in steady-state. Remember, you only have to get to 2/3vcc to terminate the pulse.
But like I said, I never tried it with real parts. Maybe if I have time one evening...
Add that to the leakage and you get 12M*.2UA = 2.4V. For a 15V operatoin, you have 12.6 volts at the threshold. You'll have to adjust the series resistor to account for this lowered voltage, but there is still pleanty of headroom.
Again, just from a thoeritical standpoint.
BTW, National sets the max value of the resistor at 20 MΩ, so I think we are in good shape.