Recently, I got to exactly 5000 reputation points. According to the privileges page, this should give me the ability to approve or reject tag wiki edits, which was confirmed with "you have already earned this privilege" in the popup:
However, obviously I didn't receive the privilege, as I still couldn't get access to the suggested edits page (click on the image to see it full-size):
I deleted the temporary data and did a fresh log-on, so this shouldn't be a caching issue.
I was immediately granted the privilege after having more than 5000 reputation, so either the algorithm or the description of the privilege seems to be inaccurate: The privileges page suggested that I had already received it. Furthermore, the suggested edits page explicitly states
[...] When you have earned at least 5000 reputation, you will receive the “approve tag wiki edits” privilege and will be allowed to view this page. [emphasis added]