Hi, er... (I cannot read your name, so forgive me for not mentioning it), The word "out" in this case goes with "here," as in "out here." Meaning, the person had to drive far "out" or outside of his city or town or village or neighborhood to get to where he is now. It cannot be "drive out" because that phrase means to force something out of a place, for example, "to drive the invaders out of your country." It also cannot be "the way out" because that would refer to something like an exit or an escape path. Haha. Hope this helps.

It's "drive out (to somewhere)" it means driving to somewhere far away but since with "here" "to" isn't used, it's "drive out here". "All the way" indicates distance. So you could have said "I drove all the way here." And it still would mean the same thing. Sorry, I can't think of another way to rephrase this sentence. Maybe someone else can, have a nice day! :)