Why would the runway separation for parallel triple simultaneous precision approaches be dependent on airport elevation?
What the text means is for triple simultaneous approaches for airports above 1,000 feet MSL, the FAA needs to conduct a case-by-case study. I.e. there is no automatic approval, yet.

Also, but not related, for airports below 1,000 feet MSL, reduction in separation from 5,000 feet also requires a case-by-case study.


  ... impractical or the...


I do think the paragraph you quoted can benefit from better punctuation.



Runway-to-runway separation does increase with elevation due to increased ground-speed and reduced reaction time.

The case-by-case study is usually done via numerous trials.

As for why 5000 feet, I was stuck in a loop between Annex 14 Volume I, PANS-ATM (Doc 4444), and the AC 150/5300-13A. Each quoting the other. Literally.

The Manual On Simultaneous Operations On Parallel Or Near-Parallel Instrument Runways does indeed discuss reaction times.

So, it's fair to deduce the increased separation is to give more time for ATC to notice any deviation and have time to react.

The FAA AIM does confirm the OFZ (Obstacle Free Zone) increases by 20 feet per 1000 feet elevation. The OFZ is in turn quoted as the reason for the runway separation increase the higher the airport is in the AC you quoted.



In short, increased elevation/ground speed requires case-by-case study to approve or bring down the separation. It's down to the reduced reaction time and airport equipment—e.g. radar accuracy, refresh rate, and so on.

The values themselves seem to be derived from trials plus added factor of safety plus rounding up. I can't find information on the trials.

Separation is not reduced with increased elevation, it's the opposite—if the airports (low and high) have the same exact equipment.