Why doesn't my custom library load?
You are missing a colon after depx-slides:

dexp.slides:
  version: 1.x
  css:
    theme:   
      css/plugins/font-awesome/css/font-awesome.min.css: {}
      css/admin.style.css: {}
      css/plugins/rs-plugin/css/settings.css: {}
  js:
    js/dexp.layerslider.js:  {}
    js/plugins/rs-plugin/js/jquery.themepunch.revolution.min.js:  {}
    js/plugins/rs-plugin/js/jquery.themepunch.tools.min.js:  {}
  dependencies:
    - core/jquery
    - core/jquery.ui.draggable
    - core/jquery.ui.dropable
    - core/jquery.ui.sortable
    - core/jquery.ui.dialog 
    - core/jquery.ui.tab


The YAML is pretty strict about format. You can run it through a linter like YAML Lint - that is how I noticed the colon was missing. 

After making that change, clear your cache and require your library (either in the info file or by attaching it with #attached or attach_library in a twig file) it should work.

The official docs page has all the info you need about attaching libraries, but the YAML must always be correctly formatted.

That YAML Lint tool, by the way, works for any YAML. If you ever work on a routing, permission or other YAML files, it can check if it is valid or not which is the first step to debugging YAML - simply eyeballing it is not good enough - use the tool that will just tell you. There is an npm package available to run it from command line (I do recommend).