You need to be more specific. There are MANY breeds that can run 2-5 km daily. There are also many breeds for which 5 km isn't even enough.
What kind of grooming and training do you have in mind?
All I can tell you now is to look for a slightly older dog, at least 1 year old... puppies cannot run that far because it will damage their joints. Avoid brachycephalic dogs as well -- that is, dogs with "flat" noses (pugs, boxers, etc.)
At obedience training, I was informed by the trainer that my border collie is bred to run up to 75 miles a day!!! After I peeled my jaw off the floor, I informed her that we wouldn't be running that far. I don't think she actually expected us to do that - just was trying to point out that I need to find outlets for all that energy.
I second what others have already said: what sort of running activity are you planning with your dog?