Will you have five full days, or will part of one day be the day you arrive in Provence?
Be forewarned, there is a lot to see and do in this area. I spent two weeks there and never made it to Avignon, and I was busy!
Plan at least one day for the Luberon. You will want at least one full day for the impossibly charming villages, but you will probably want at least one day more for visiting vineyards.
Plan a day for Avignon. You may want to take a detour for a couple hours to see the impressive Pont du Gard.
Arles is smaller than Avignon, but if you are interested in its Roman history, there is plenty to see, including the very informative and interesting archaeological museum and the wonderful arena, still in use today.
I would highly recommend a day-trip to Les Baux de Provence. This is a ruined castle complex on the flat top of a hill, complete with mock-ups of medieval siege weapons, surrounded by a somewhat lunar landscape, overlooking a very pretty if touristy village. But the single biggest draw might be the stunning territorial views from the top. I wouldn't miss it. This could be easily combined with a morning stop at St-Remy's farmers market if you can go on a Wednesday (market day). If not on a market day, you could probably mix it with a relatively brisk visit of Arles (which has its own huge farmers markets on Wednesdays and Saturdays).
Just a note, I found myself making a point of hitting a farmers market nearly every day. They are great places to pick up a great picnic and really a treat just to walk through. They start around 8:00 or 9:00 (come early for easiest parking and best pick of the produce) and are all done by around noon.
If you want to go to the coast, my pick would be tiny Cassis. It's somewhere between 1.5 and 2 hours each way. It has a tiny, unimpressive beach, but its big draw is boat tours of the calanques, inlets in rocky cliffs. It is absolutely gorgeous. The little village is good for a walk-around as well. I would make a decision about whether to visit after you arrive. I think you will find yourselves busy enough, but if you feel you have the time, Cassis is a worthwhile visit.