Hi. Why don't you use a 4017 decade counter, the chip used in LED chasers. Set your 555 pulse for 1 minute, and set the 4017 to count only to 6, by connecting the reset input to output 7. Then, connect your light, via a relay and npn transistor, to one of the first six outputs, output 1 would do fine. When this output goes high, it will turn your light on, and for the remaining 5 outputs, your light will be off. Since each output will turn on for 1 minute, that should work for you.