No fig will survive in an detached shed without the use of a small heather,to keep the interior about 30F+,in your zone 5.
Once you secure a safe heat system,then the cold hardiness does not matter any more and you can even grow Black Mission if you want.
Without the heather,the roots of the plant will die much faster,and at milder temperature compared to the trunk and branches.

It all depends on the coldest temperature you get in the shed and for how long i.e. the coldest temperature in the shed for a sustained period (& not just a short dip in temperature. Most varieties could die at temperatures around 12F if just left in the shed without any extra protection and geothermal heat trap and hardly any may survive a sustained temp under 4F in the shed (if not under protective cover with some heat source or trapping ground heat). If any survive (fat roots survive in the pot), it will take most of the summer to green-up.
I am in Zone 5a and have been using a small heater in the garage and a wireless temperature reading to ensure safe temperature above 23F.
I hope to get a chance next fall to make arrangement for setting up a temporary styrofoam enclosure (from November to March) inside my unheated uninsulated garage and then use a very small heater that turns on at a preset low temperature.

This way I do not have to look for a very cold hardy variety but concentrate on early ripening varieties.
That is my opinion. Hopefully somone will give a better answer.

Hey Tony,
Been there done that. ; )
zone 5 here also temps got cold this season 15 below coldest.
Several years ago 23 below zero.
Many years ago i tried storage in outside shed they died .
In a good winter they may or may not make it, cold winter forget about it as shed will quickly be same temp as outdoors.
Martin
Near Chicago,Illinois
Zone 5

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