No the resurrection does not need to begin by a certain 5790, or any other specific date. Eschatological predictions are matters of personal conjecture; not definitive views of Judaism.
In the words of Dr. David Berger:
I am more than a bit disturbed when respected Orthodox organizations disseminate material stating as undeniable fact that the redemption must come
before the year 6,000 in the Jewish calendar. Other messianic dates in the Talmud have passed, and Maimonides—in an explicit effort to discourage messianic calculation and obsession—made a point of emphasizing that even Hazal did not have a tradition regarding these matters (Hilkhot Melakhim 12:2). Many years ago, a friend told me how a classmate of his in a traditionalist yeshiva had told him that if he would be alive in the year 6,000 and the Messiah would not have come, he would throw his tefillin on the ground and stomp on them. It is worth reemphasizing the prophet’s declaration: “For My thoughts are not your thoughts, nor are My ways your ways, declares the Lord. But as the heavens are high above the earth, so are My ways high above your ways, and my thoughts above your thoughts” (Isaiah 55:8-9). [i]
This would apply to the 6000 year mark from which they are counting back the years for the resurrection of the dead, in addition to the point at which the resurrection itself would begin.
[I]Tradition: A Journal of Orthodox Jewish Thought Vol 39 No. 2, p 77, note 2.