The Starter Set adventure (Lost Mines of Phandelver) fortunately happens to be a great level 1-5 mini-campaign, regardless of your experience level.
Even as an experienced DM, you'll enjoy running it. And for new players it's the best 5E option by a lot.
I used it to teach a gaggle of 13 year olds to play D&D for a friend of my wife's. As far as I know they are still at it a year or so later.