The good news is that you've got more than enough room. The bad news is that you're not going to be able to grow something that gets really big in your Zone. Bamboo is hardy, but most of them will either not survive your winters, or will defoliate and have the culms killed, although they will put out new shoots in the spring. The hardiest bamboo that I can think of that will put out relatively large culms is Ph. nuda, which is hardy down to minus 20 F, but it will lose much of the aboveground growth each winter. (The "hardiness limit" refers to the lowest temperature that won't kill the plant entirely...it will still look sad in winter). The maximum diameter for nuda is under 2". If you've seen big culms at the zoo, they were probably imported from Vietnam, Thailand, or China...not grown locally. I'm not trying to discourage you; there are a fair number of folks who grow bamboo in Zone 5. However, you have to accept the limitations of where you are living, and that you're not going to be able to have evergreen bamboo or expect it to get huge.

Define Big? Like kudzu9 has pointed out, partial or complete dieback is a reality.
Phyllostachys Rubromarginata could be worth a try.

All that I can tell you is that at the St. Louis zoo the most common bamboo they grow is Phyllostachys aureosulcata the Yellow Grove Bamboo. It is growing all over the zoo in unsheltered locations

I got my so called p nigra henon which turned out to be (I think) some sort of yellow bamboo from this place, bamboogarden. The link below shows timber bamboo that may grow for you (try to keep it near your house if possible on the south facing wall (if you don't mind it growing there!), that way it's more likely to ovewinter and the residual heat from the house can help it survive and get bigger culms- plastic and black plastic can help it overwinter too.
Just make sure to NOT get the smallest size bamboo, I did and it croaked on me! Plus it spreads much faster if the bamboo is bigger. Good luck! Hope this helps. :)
http://www.bamboogarden.com/Timber%20Bamboos.htm

This may help you in deciding what bamboo to grow.

http://www.bamboogarden.com/care.htm