The roots are also a bit brittle and snap apart easily too - so in the spring when you're not dealing with a lot of awkward foliage is an ideal time. Get your new transplant hole in the backyard prepared and ready before digging up the plant. Get as much of the root ball as possible and it should do just fine. If some root pieces break, plant those too and you'll likely get new plants.

I am from zone 5 also. I find that my bleeding heart blooms profusely in the spring, like duluthinbloomz4 says. Thereafter, it starts to die back. In fact, I trim off the larger branches, as they tend to droop and look somewhat unsightly. I look at them as similar to other spring blooming plants, in that they put on their growth in early spring, have their fertilization period, and then regather their strength shortly after and finally start to go dormant during the really hot August days. That being said, I would take a differing viewpoint from duluthinbloomz4. I think that I would be tempted to let it die back somewhat this summer, trim off the branches to a manageable size, leaving some of the healthier smaller branches on, and move it this fall or late summer. Remember what duluthinbloomz4 says about the roots, so take as much earth as you can with it. Water it well, and then let it finish going into complete dormancy. This way, you won't disturb its rapid growth in the spring, and should get a wonderful floral display next year.

The other comment to be made is to consider the light requirements of the plant. I find that I get a nicer plant if it gets some shade and sun mixed. I have mine on the northwest side of the house. It is HUGE, and I get new plants coming up yearly. It seems to be happy there. Of course, any plant will perform its best when it is happy.