I have three category pages (category-5.php, category-6.php, and category-7.php) and I want each one to have a different look if a single post is viewed, is it a simple as creating 3 copies of single.php? like single-category-5.php, single-category-6.php, and single-category-7.php?)

Here’s a list of the accepted templates:

And templates for categories:

And a overview of the hierarchy of templates:

I’m not sure if that’s quite what you’re looking for.

I am just going through some tutorials this past week and I don’t think that’s how you woudl do this. i am very new to php and WP template design but from what I understand you would have one single.php post, that perhaps would call a diffrent style depending on the class /catogory called.