Five days is really not enough to island hop and split between islands. Pick an island and spend your time there. Why Santorini? It's one of the heavily touristed and expensive islands to visit even for June.
What are you looking for in a Greek Island Experience?
If I am reading your itinerary correct you have June 23, 24, 25, 26, 27 free which is the five days. Are you planning on returning to Athens on the 28 and flying out the same day? If so you are pushing your luck. Most people recommend returning to Athens at least one day before departure in case of delays, cancellations or strikes.
A little more research on your part and/or more info can help you make better choices.