For Lightroom 5, the Plugin Manager gives the following error upon trying to enable Palette Plugin (V2):
Palette Plugin uses features which were only supported starting with Lightroom 6, CC 2014, or Lightroom Classic 7.0. To get the most of your Palette kit with Lightroom, please consider updating to Lightroom 6 or to Lightroom Classic. For more information on which versions of Lightroom are compatible with Palette, see this article.
You may still use the Lightroom 5 profile type within PaletteApp (from the "Select a profile type..." screen) which allows you to control various useful features within Lightroom with Palette buttons and dials.