Hi Devin,
As a former Otoe Co. resident (born in N.City!) I can tell you that you will not have any trouble growing the red Raspberry. It will thrive no matter what. You are in prime territory for it, perfect soil and climate.
Now, the Ebony King is another story. Blackberries are mostly a Southern fruit; most are not very cane hardy in zone 5. Next time you go to purchase berry plants, make the distinction between black Raspberries and Blackberries. One of the problems that you have just encountered is inappropriate plants often sold by large stores. The corporate buyers either do not care or simply do not know- either way, it is wrong and not fair to the customer.
So...do not put a lot of effort into your Ebony King- it is terrific down here in Texas, a dog for you up in Nebraska. As someone mentioned prior, go get some more of the reds...put a row in. You will be glad you did. So easy to grow and very productive. You will get some berries this year but next year- JACKPOT! I might also suggest you go online and buy these. You can get them quite cheap from Simmons Plant Farm (simmonsplantfarm.com). I would put in arrow of about 25 or so. Be on the look out for a gold Raspberry! There are several cultivars such as Fall Gold- they have remarkable flavor, more sweet than tart. Just as easy to grow as the reds.
As for care, just keep them watered the first year- once established, they become pretty much care free. If it gets super dry in the summer, hit them with water 1X per week if they are carrying a load of fruit. I do not remember having much in the way of pests or disease bothering them. Just remove old, worn out looking canes every year and you will be fine. The row will get thicker each year and you will be able to expand your row quickly by digging suckers. After about 3 years, you will be a pro at growing Raspberries and everyone in town will be your best friend once the fruit starts coming in! Trust me, regardless of what you read, growing Raspberries is easy and does not require a huge amount of thought- as opposed to Blackberries that I now grow (about an acre of them- I sell them).
Though I can honestly say I do not miss living in Nebraska, I DO(!) miss being able to grow Raspberries (and Peonies and Lilacs!). Since all my family is still in Ne. (Talmadge and N. City) I am able to enjoy seeing these things every now and then.
