Is there any way we can tell how many users have been active on Worldbuilding over a period of time, like, say the past 5 minutes/hour/day?
The answer to the question as asked is: Not directly.
The site is currently doing very well in terms of activity.
Diamond moderators have access to "analytics" data, which includes data like number of visits on the site per day. (The data is available down to a resolution of one day, so doesn't really meet your request of being for minutes or hours.) The specifics of analytics data cannot be shared in public.
However, having gone in and looked at some of it just now, I can state as much as that by almost any reasonable measure of site activity (number of visits, number of questions and answers, number of votes cast, number of edits, ...) we are currently at or close to all time highs. This includes the initial surge of activity at the beginning of the public beta period, which we have actually in some ways surpassed. Good job, community!