Greyhounds are not really distance runners.
To the OP- like others have said, unless you want to wait 18 months+ until a puppy is old enough to run with you (running too young is very damaging to the growing joints), then go for a young adult rescue. About 18 months to 3 years old. Then condition, almost any fit medium to large breed (not giant breed) should be able to run 5-8 miles in good weather. Remember that dogs are more heat sensitive than people so during warmer months, you'll need to run very early or very late or leave the dog at home (maybe running 3 miles with the dog and 3 miles without the dog).
You want to look at your living situation- some breeds, like Dobes, are nearly impossible to rent with. If you plan to use a dog park or doggie daycare, you may want to avoid breeds with a tendency to dog aggression. Basically, there is a lot more to choosing the right dog than picking one that can run, simply because so many of them can run that the other aspects or traits should be the deciding factor.
Some breeds that I think make good running partners (but may or may not fit other parts of your life): Hound dogs like black mouth curs, walker coonhounds and other hounds bred to hunt (run over distance), pit bulls and mixes, labs (especially if kept lean), ACDs, and in general the sporting breeds. Any dog about 50 lbs plus will be a good deterrent, you don't really want an overly protective dog since that can backfire around people in the park for example or even rescue workers if you had an accident. I mean, you don't want to be out jogging and get hurt and have your dog bite the paramedic...
I went to the shelter looking for a running partner, told them that and pointed out a large dog that I'd seen on petfinder. They said he was a very high energy dog that would do great with running. He's a Rhodesian Ridgeback mix and for the 2 years that I was really running hardcore, we did about 3x per week at 4 miles and 2x per week at 8 miles plus daily walks of 30 mins each morning and one day per weekend for a long (2-3 hour) hike in the woods. I have slowed down and he's slowed a little, more to match me than anything and of course, the summer heat right now, so we do a few 30 min walks daily and then aim for a few miles of hiking on a weekend morning when its much cooler. Running alone isn't enough, you have to vary things and also work their minds.