Moshiach is coming – isn’t he?

To answer your question, we must first define the term “exile.” In secular terminology, exile is defined as ‘the state of being barred from one’s native country, typically for political or punitive reasons.’
This is not the true Jewish connotation of exile. The Torah concept of exile includes being sent out of our country, but not only. The land of Israel is not called ‘the Holy Land’ as a sentiment. It truly is holy, and when the first and second Temples, the Batei Mikdash, were standing, G-d’s presence was felt there by ongoing miracles. Exile for the Jewish people means that the Temples were desecrated, G-d’s presence was not manifested by these miracles, and as is still true today, even though many Jews live in Israel, thank G-d, many Jews still look to the nations of the world for approval, and there is not enough awareness of the Divine plan.
Regarding the fifth exile, there is much discussion among the commentaries, but the whole concept of exile can be on a spiritual plane, and does not have to involve being under the actual physical rule of a foreign power.

The important thing is, what are we doing to bring about redemption from our personal spiritual state of exile?