i'm guessing 5
Not quite.
One shot = all the electricity from all the power plants on earth for the lifetime of the universe X 100.
Or
One shot = converting all the mass of Mount Everest into energy using E=mc2
And because of the size of the thing (160km sphere) if it were to actually use Mt. Everest-sized pellets, there's not exactly a ton of space inside the thing for ammo. So the Hypermatter discussed in the video (owing to density=mass divided by volume) would either have to be extremely dense or somehow stored in a pocket dimension somewhere other than the Death Star.
...but that's another physics problem for another day.
Ross might be closer with his guess of "five" than we gave him credit for; he just anticipated the question of "How many times can that thing fire before the ammo reserves are depleted?"