“Aren’t they supposed to be mount from 5 to 8 feet above ground?” No. Whatever height above ground you chooose, you configure in the station setup. Tempest uses that information in various calibrations and adjustments. See Tempest location : 10 meters above ground? et al for more details.
Any “all-in-one” class of weather instrument (like the Tempest) rarely has an optimal height since different parameters have different standard heights, so, as @vinceskahan stated, it is advisable to choose the height depending on what parameter you are most interested in. Also, wind readings are greatly affected by surrounding terrain, foliage, structures, etc. so the optimal height for wind readings is often not attainable without choosing a different location .