Growing Chinese Herbs

I am trying to grow Chinese herbs. I am in a Zone five, but have a small greenhouse and it gets hot in the summer. I have two questions. Do you have a list of Chinese herbs, I am having a hard time finding out if the angelica is the right sub-species. Bai Zhi is is the Dahuricae type right? but there is another type called Sinensis. If It is hard to come by would you know of a very similar type? I can sort of get by on guessing names but if there is an easier way.

Bai zhi is Angelica dahurica, while dong quai is Angelica sinensis (renamed Angelica polymorpha sinensis)
I don't know if you have our catalogue, but if you do, you can pick out the herbs that would be hardy outside in zone 5 by checking the letter code listed beside the latin name. A capital "P" means the plant are hardy perennials in zone 5. If there is an "A" beside the name it means the plant is an annual and its hardiness is irrelevant.
Our year 2000 catalogue will be ready to mail soon and it will list the hardiness rating for all of our perennial herbs. You might wish to wait for it. But in any case, do request our catalogue – you can do it on our website (https://www.richters.com).
Also the catalogue mentions if the plant is a Chinese medicinal or culinary plant and therefore you won't have to guess.

The other question is of the chinese herbs available, would most of them live in Zone 5? How well does a greenhouse work for keeping warmer plants alive?

A greenhouse works well for keeping frost tender plants over the winter. Some of them may have to be kept cool to do their best over the winter.

I am rather new at growing herbs, so I hope these questions don't sound too silly or too vague. I just want to find out how realistic the growing idea really is.