5 minutes is a little long for a 555 time, but I think it will work if you use a low-power LMC555 CMOS timer along with a ceramic capacitor, both of which minimize leakage that would affect the timing.
Below is the LTspice simulation of the circuit:
The timing capacitor C1 is a ceramic type such as
this.
Note that the output pulse interval (green trace) is extended by 300s when the reset input (yellow trace) momentarily goes high and resets the timing capacitor voltage (red trace)..
The 555 output is driving a P-MOSFET to switch the load voltage.
You may have to tinker with the value of R1 to get the desired interval time.
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