I wouldn't want to jog (on-leash) with a 5 month old giant breed. That's a lot of repetitive impact on growing, immature joints.
It isn't so much about the pace/speed of the jogging as it is about the fact that by running on-leash (or heeling next to you) she is running in a straight line with similar movements each step and similar impact each step. Particularly if you are jogging on concrete sidewalks (the worst) or asphalt road or path, the impact is greater than on dirt or grass. Personally, I wouldn't run a large (and she's on the large side of what most people think of as large breeds) puppy until 18 months minimum.
Compare it to the overuse injuries seen in young athletes (Little League pitchers for example) where a 12-yr old who pitches a lot of games ends up with injuries not usually seen in college or pro players until after several times as many games.
But you CAN let her run- you can run around in a field, she can run in a fenced area or you can get a 50 foot leash or long line (a horse lunge rope makes a good long line and it easy to find at farm stores like Tractor Supply), anything where not only is she setting the pace but is also both varying her movements and is on a softer surface (grass, dirt or sand).
Swimming is great exercise if you have that option. Hiking where you go up and down hills also give some variety and extra workout (although I wouldn't overdo hiking either for a few more months). Long walks broken up with training sessions to work her mind. Visit public places that allow dogs - college campuses, outdoor restaurant patios, many camping and outdoor type stores, many home improvements stores (many Home Depots and Lowes allow leashed dogs, ask the manager), outdoor festivals etc - after a good walk and do training and socializing there. The extra sights, sounds and people to meet will tend to tire her out too and is great practice for being a well mannered dog.