Not nearly enough. The timer changes state when the timing capacitor is charged up (to 1/3 Vcc). If you then remove power to the timer, the 555 cannot discharge the cap.
There are adjustable and programmable cycle timers on ebay that will do what you want, but 1 second out of 300 is a very high duty cycle. This is one of the reasons I don't like the 555 for multi-minute periods, but it can be done. A modified version of the standard 555 astable can be tweaked to a 300:1 duty cycle, but the timing cap will be huge and the long period will vary with room temperature.
Another way uses the CD4060 to make one pulse every 256 counts. A 5 minute cycle would produce a 1.2 second pulse.
ak