Well Ludvig, considering I am in a z8, my comments on z5 or z6 cannot be based on direct experience. Being conservative, the chances to grow eucalypts in such restrictive winters would be low in my opinion, even using the hardiest species and thinking of dieback perennials.

Still, it all depends on local conditions and how effective protective measures can be. E. neglecta seems to have its limits around -15ºC (sometimes lower, it largely depends on duration of freeze), but seems to coppice well too. If planted in a place where soil did not freeze for too long and with as good insulation as possible for the base of the tree (a pile of good mulch, and maybe snow also helping) during the worst of winter, it could have some chances.

A south facing slope, protection from chilly wind, no shade, mulch, and hope. And luck. There are many "if's".

E. gunnii (subsp. archeri and allied species E. urnigera), E. parvula, E. perriniana could be some other species with similar hardiness, good coppicing ability and relatively fast growth (which would happen during the long day periods there at high latitudes). But beyond z7, "everything is mostly a matter of luck" in my opinion.