Handling URLs in WordPress application

../directory1/directory2/directory3/css/stylesheet.css should get you there if I am reading your description accurately.

However, I would be very cautious using relative links in WordPress. They do not always work the way you’d expect because a lot of ‘directories’ don’t actually exist. They are fabricated by WordPress and mod_rewrite. The two conspire to lie about filesystem structure. For example, there is no http://blog.com/category/cat-a. A relative link on that page would be broken.

You are better off using bloginfo or site_url and constructing absolute URLs. site_url would the function to prefer.

$url = siteurl('/directory1/directory2/directory3/css/stylesheet.css');