Upvote:3
After you entered UAE, you can check the validity here.
Upvote:6
Yes, you can stay longer (up to 90 days!). This is how the visa works.
They put a deadline on when you can enter, for a number a reasons - knowledge of numbers, validity of passport, relations between them and your country, whatever - but there's a final date on which you can enter. That's the May 7th.
Once you arrive, your visa 'begins'. It'll run for 90 days from when you arrive. Note the distinction - it's not three months, but 90 days, be careful when calculating.
If you'd like a slightly more official source than me, Emirates lists the visas and notes " 90 days from arrival date" as well.