Create a filterable, sortable admin view that produces front end block The goal is to produce a single block to go on the homepage with 5 linked terms from a single taxonomy vocabulary. These terms would be selected and then ordered in an admin interface by a content administrator. The taxonomy vocabulary itself my have 30-50 terms.

I thought I could create an admin view with an exposed form to select the terms and then apply draggable views to the results, but I am having trouble combining the exposed form and draggable views. I am also having trouble turning the results into a block. 

Happy to ad more info if this is vague, but all of the views I have set up have been so wrong I did not want to waste anyones time by posting them here. 

Would views / exposed filters / draggable views be the right way to go about this or is there a better way? I'd rather not install something huge like panels to make this happen.
Another way to do this would be to install 
https://www.drupal.org/project/term_queue

This contrib module gives you all you need.

Here is a screenshot, admin interface to the right, front-end block to the left.

The module provides a block automatically, for each term queue, you simply need to place it.

Good luck!