Lisa,
I am not aware of any that would be hardy in your zone. But, the tubers of most hedychiums and curcumas are easily lifted and stored during the winter. I recommend that you start with White Butterfly Hedychium as it is one of the most hardy and vigorous growers.

After posting this I found an old shade gardening book. In it there are a few gingers that are listed for zones 5/6. However, I didn't see anything like your pictures! WOW! The ones they in the book are all low like ground covers. For example, there is Asarum arifolium (arrowhead ginger), Asarum canadense (canadian ginger), Asarum europaeum (European ginger), and Asaurm splendens (chinese wild ginger). None of them seem to flower at all. They don't even appear to be in the same family.

The Asarums are not in the same family or even closely related to the tropical gingers (Family Zingiberaceae).

For zone 6, you should be able to grow any Roscoeas or Cautleyas (try Roscoea auriculata or R. purpurea or Cautleya spicata). Also, Zingiber mioga would be hardy there. I have more info on them at the link below, but I cannot grow them here because the weather is too hot and muggy in the summer. I have some mail order sources for them listed on my website.

I don't know if any of the Hedychiums would be hardy zone 6. I scanned through Branney's new book on "Hardy Gingers" and the most cold tolerant ones according to him are H. coccineum, H. densiflorum, and H. forrestii which he rates as hardy down to 0 degrees Fahrenheit minimum temps. Officially at least, zone 6 can get down to -10 degrees. If your location never gets that cold, you could try a few of the "zone 7" Hedychiums.

I also have an article on my website written by a guy in Michigan (zone 5) who overwinters Hedychiums in his basement. He explains all about it in the article.

Here is a link that might be useful: All About Gingers

For what it is worth: the hardiest Hedychiums I am aware of are H. spicatum and H. densiflorum. H. forrestii is probably a variant of H. spicatum (you might try asking David Constantine or checking his website). They are both naturally deciduous, unlike many Gingers.

I suspect they are hardy to USDA z7, and I'm pretty sure they tolerate a few degrees below zero Fahrenheit. You might be able to push them a little by mulching them. The risk to them is that the rhizomes--which unfortunately are prone to creeping along or just under the surface of the earth--must not freeze. If your winters are dry (and they probably are) you might be able to protect them with a thick enough leafy mulch before the first freeze hits. This is a long shot but there are people who grow all sorts of surprising things by piling vast amounts of mulch on them.

Gingers are hard to move in and out of doors, the reason being that they are one of those plants that transplant poorly dormant. If the rhizomes are damaged while they are dormant, they might rot. If growing in earnest, you can take small pieces of rhizome and get them started with no problem, usually. I learned about this the hard way, having wrecked my clump of Zingiber myoga trying to divide it dormant. It never fully recovered, and is only a shadow of its former glory. It has taken years to recover as much as it has.

The guy in Michigan might be doing something tricky like plunging the whole pot (so as not to disturb the rhizomes too much).

I don't know where Cautleyas and Roscoeas become possible. They do not deal well with high heat. My own climate has fairly cool summers so that is not a problem. Even in Seattle, tho, they flop over in particularly hot weather, and won't resuscitate until the weather cools down.

Cautleyas are probably intermediate between Hedychiums and Roscoeas. Not quite as alpinish as Roscoeas. There are all of about 3 species. Very tropical-looking but not quite as showy as Hedychiums, or as vigorous or lush.

Zingiber myoga is weirdly hardy for a Zingiber. Easy to grow, too. It would probably need a mulch, tho. You can harvest it and use it just like culinary ginger; its the ginger you find in sushi bars stained pink (the pink traditionally from shiso leaves) called "myoga" (fancy that). The Japanese tend to harvest it young but you could harvest it fully ripe if you want something stronger. The flowers are, alas, small, and almost hidden under the leaves; they grow on short stocks at the base of the plants. This is typical of the genus. The flowers are yellowish or off-white. The Japanese have been known to dip them in tempura batter and deep-fry them.

NOT A GINGER, but looks vaguely like one, is Pollia japonica, actually a member of the Tradescantia family, which also happens to be weirdly hardy for its own family. Look it up on the internet. It is easy to grow to the point of being weedy and is almost certainly hardy in USDA z5. One of its relations is cultivated in the south and (mistakenly) called "Blue Ginger".

Asarums are not Gingers and it is unfortunate that people keep calling them such. Their rhizomes reminded someone of Ginger (someone who doesn't really know what Ginger smells like) and the name stuck. Not only that, but the more beautiful of them are probably not ironclad hardy in your climate. Actually they do bloom; they are not as showy as real Gingers and the flowers are hidden under the leaves, but some of them have blossoms that are "interesting" and kinda pretty in a grotesque way. (Many of them are slug pollinated so what do you expect?). Some of the Chinese species have rather striking leaves.

Don't know if this will still reach posters (3 yrs later), but I too am a MICH Ginger Newbie. Have not tried to grow Any yet but was researching Alpinia Z's and Curcuma Siams. I think, from what I'm reading, I may try the Butterfly Hed. I truly am grateful to this site for all those can give us this Much Needed advice.

Many thanks!!!

To the Original poster, I have Canadian Ginger. It is an entirely different plant!!! Groundcover only!!!