Although this is possible, you really don’t want to load multiple versions of libraries as it’s going to make your site slow to load.
You could try and use Bootstrap with a pre-processor like SASS with mixins to target just your plugin code and not the rest of the theme.
FontAwesome 4 and 5 seem to use different prefixes fa- and fas- so you could load FA5 before FA4 as per this post.
Lastly, you could