This is impossible for us to tell you, but from everything I've heard it is very possible that test dates could fill up. I would look around on the GMAC website and see if dates have started to fill closer to that June 5th deadline and make a decision.
You always have the option of taking a date and paying yoru $250, and if your some reason you don't use it, you will get $80 refund if you cancel early enough. I would recommend that you do this method b/c it will give you a start to your studies and date to put on your calendar as G-Day. If you REALLY plan on taking the test, then why don't you just book the date early.
I've heard of people waiting till last minute to book their test, and then realize the day they wanted is filled, and had to travel for the test or push it back. I took my test around August/November (GMAT season) and i booked it 9 weeks in advance. There were already days filled b/c people wanted to avoid thanksgiving, christmas, new years, and still make R1 & R2 deadlines.
New to the GMAT Club? <START HERE>
My GMAT and BSchool Tips: