Perennial zone 5, minimal watering, small and bushy to make a privacy screen, not a blueberry and no woody vines...

Whoo boy. Only thing that sprang to mind was a tea bush, but I don't think any of those will survive in zone 5.

Oh wait, how about thornless blackberries?

Blueberries actually make a very attractive edible hedgerow. The drawbacks I see are 1) you have to make sure the soil pH is proper when you plant them, and adjust as you go to make sure it stays in the correct range. Not all that hard to do (well, most of the time); and 2) they're kind of slow growing, it would take a few years to fill in and yield a good barrier; and 3) of course, deciduous, so for close to half the year you would have some view of the neighbors.

I often see blackberries for sale around here...maybe a thornless wouldn't be a bad idea. I have a couple blueberry bushes from last year that I planted, so if they pop up this spring...that may be an option. Most people I've talked to locally can't seems to grow them well. If I didn't go the edible route, any other possibility?

Just in case you didn't know there is an Edible Landscaping forum here that might provide you some great tips in all the info there.

If you want to forgo the 'edible part' then the Landscapeing forum would be the place to start.

Otherwise consider Edible Shrub Hedging

Dave

If you don't want to go edible, a regular box hedge will be the easiest. That stuff is impossible to kill short of soaking it in roundup, so harsh winters, not a problem. Getting hacked to the ground, not a problem. Attacked by any insect you can name, not a problem. Box hedges just laugh at your puny attempts to kill it and keep on growing.

Here in AZ, citrus and pomegranate would both work. I can't think of anything comprable.

If you don't have a problem with yellow jackets, I'd plant arborvitaes, along the fence...then something else in front of them. They'll give you the privacy you want, are inexpensive, grow fairly quickly and don't take lots of water. They will provide privacy year round, but they do sometimes, attract yellow jackets.

In front of the arborvitae (think layers, if you have the space) add some butterfly bushes, especially on the ends. They're beautiful, bring in butterflies and around here...calm down any yellow jackets that do stop by. They seem to get 'very happy' around butterfly bushes :)

In between, you can have edibles or just more shurbs and perennials. My mom has a beautiful butterfly garden, in her back area, where she also grows herbs and a few veggies. She has her fruit in another area.

You could go for a mixed planting. Amelanchiers (service berry/June berry) would do. Also red and black currants and thornless gooseberry varieties. Cornelian cherries. Elderberries. Seaberries. Maybe even a tall perennial like lovage, fennel, cardoon, seakale. They will die back in winter but provide screening and edibles in summer. If you are prepared to mow off shoots which grow out of the row you could have some Jerusalem artichokes. Crab apples. Chaenomeles (flowering quince). Hazel nuts. Native plum species. Unfortunately I can't think of any evergreen edibles which are hardy enough. In my climate you could have bay or rosemary in there but not, I think in z5. I would try this question on the Fruit and Orchards Forum too as the people there are US based and know their local varieties better than I can tell you.

You could also do a mix, blackberries with something evergreen such as arborvitae. Currants are another edible option or even raspberries.

Blackberries, repeatedly mentioned above, can be a lot of work and a properly trained row along a fence will not provide privacy. Also iffy in zone 5. Long laterals will grow into the neighbor's yard and drop fruit in season.

asparagus? They can get 5-6 feet after a few years.

I found this link that might help you ... and several of these are edible.

Here is a link that might be useful: Zone 5 vines