I am _guessing_ here based upon an understanding of physics and mathematics, rather than knowing the industry standard used, however:
"maximum demand over a 15 minute period continuously recorded over a 30 day period" means the peak value of the '15 minute rolling average' recorded over a 30 day period.
A 'rolling average' is a _continuous_ function; at each instant in time you have the power being used _right now_ (the instantaneous power) and the _average_ power being used over the last 15 minutes.
As a mathematical absolute truth, you _cannot_ generate a continuous rolling average from discrete data; you can only generate a discrete approximation to that rolling average. As I mentioned in my previous post, if you had some poorly timed peak power pulses, the pulses might show up in separate recorded windows, but the 'true' continuous rolling average might have a 15 minute window that contained both pulses.
As a practical matter, I would bet that the approximation to the 15 minute rolling average generated from the 5 minute discrete averages would be pretty good. Basically if you take your 5 minute data, and calculate 15 minute averages, and find the maximum, you know that it will be close to the true value that you want, but possibly low.
More importantly, the maximum of the 15 minute continuous rolling average (the true value that you want) _must_ be less than the maximum 5 minute discrete average. (I have this by inspection, not proof. I am quite certain that it could be mathematically proven if the proof does not already exist.)
Thus the maximum of the 5 minute average power use data that you already have (which is _not_ continuous, because you only record the value every 5 minutes) will approximate the true value that you want, but be slightly _high_.
You now have two numbers, which in any normal situation will be pretty similar, and you know that the _true_ number that you want to calculate is between them.
If these two numbers agree closely, then I would simply take the larger of the two and call it good.
-Jon