As Paul said, it can affect zFTP but we have not seen the formula Zwift use. We do have this though:
So we know that Zwift are doing some sort of selection to identify likely max efforts and then using those points to fit to a critical power equation. Next problem is there are several versions of the critical power model, each with different equations but David from Zwift used the term “classical CP”. I’d say the two most common CP equations that could be called “classical” are the original (Monod and Scherrer from 1965) and the extension by Morton (1996). Either way, the reason that a 5min effort can affect the zFTP is that once Zwift have selected what they think are your max efforts they will fit those to the equation and the more points along the curve to fit to, the more accurate the fit.
Here is the Morton version, the blue line is the Morton equation using a zFTP of 297W, the red symbols are your numbers that you posted from your Zwift profile. You’ve said the 12 minute effort was a true max and the 5 minute number is under what you think you can do.
The curve is only accurate if the points are true max efforts, so if they are not but Zwift has still selected them for use then the curve will be wrong. As an example, using a 280W zFTP you can create a curve using the same equation that looks like this, I’ve tried to get it to pass through your 12 min power as you are confident in that effort and be a bit over your 5 minute power as your October result was higher than the current number. The red points below 5 minutes are now further from the curve so the fit is worse. If your max recorded power at the durations below 5 mins were higher, so those red points move up, you would be closer to this curve and presumably Zwift would see 280W as a better fit to the equation.
Caveat - we don’t really know which power/time points Zwift is using or if they are using this Morton equation, the original or some other variant.