How can I make cyclic 4 min. delay circuit that works on 5VDC
This very clearly calls for about any microcontroller: 
It's a discrete-input discrete-time (that's the definition of digital!) control problem.
The power consumption of microcontrollers is negligible.
Programming a microcontroller is way easier than implementing something analog that allows for such large time delays with a reasonable degree of repeatability.
So, get yourself some microcontroller board - an arduino, a clone thereof, some ST Nucleo board... the choices are endless.