I would start with all blockout days.
You can see the blockout schedules on the DLR website here:
SoCal Select AP Blockout Dates
SoCal AP Blockout Dates
Deluxe AP Blockout Dates
And also MousePlanet keeps a calendar:
MousePlanet's Integrated Blockout Calendar
That means June 12, 16, 17, 18, and 19. However, there are two grad nights on June 16 and 17. If you are OK with that, then those are your dates. If you need five
consecutive days, then it would be June 15-19 with June 15 a non-blockout.
If it was me I would rather deal with the AP holders than grad nights mostly because crowds do not bother me that much and I would still have some of my days on blockouts.
I would plan things for the AP non-blockouts that were more non-ride oriented. Like Blue Bayou, Aladdin if possible, etc. So personally I would choose June 12-16 if I needed five straight days in your time frame. That would be two blockout days on June 12-13, and three non-blockouts. I would see WOC, Fantasmic and fireworks on June 12-13 if possible - if not then see at least two of the three. I would ride Captain EO on June 12-13 as it is newish and likely to interest the AP holders on their days.