I don't know how you use blackberries. My wife cannot eat the seeds due to medical considerations so I make juice out of them, then can the juice. It is one of the easiest cannings I do, it being a quick water bath method. Just find a good recipe. The juice can be used to make jelly, cobbler, or whatever at your convenience. I did two cannings this year. Out of about three gallons I got 4-1/2 quarts of juice. Then out of about 4-1/2 gallons, I got about 5-1/2 quarts of juice. Not sure why the difference per gallon.
To keep the berries "fresh" while I was getting enough for a canning, I would freeze them and store them in zip-loc type bags. I did it two different ways. I look them and rinse them well. Some I dried off and put on a cookie sheet on wax paper in the freezer. A couple of times while they are freezing I stirred them up so they wound up frozen as individual berries instead of a solid clump. The others I just put in the bags and froze them in a clump. Both worked well for canning, but if you need to measure them for a recipe the individually frozen berries are real handy. With 5 gallons of berries, that would take a lot of cookie sheets and freezer space to individually freeze them. How you plan to use them may help you make that decision.
Hope this helps. Good luck!