Suppose I want to search for videos with duration of 10 minutes to 30 minutes, which was uploaded in 2013 and for which has more than 5,000 views, sorted by rating.
How do I do this search?
The closest thing I could think of is to use Filters in YouTube, but the options you get there are pretty limited. (Searching by exact date range is not possible.)
One other option is to use Google Video Search, with custom filters as below. Also make sure to include site:youtube.com
which will list results only from youtube.com. The only option that you will miss out is the filter by view count!
Of the above two approaches, where one misses out on view count and the other on date range filter, you need to decide which filter you will not use yet be able to narrow down the video you are trying to find and use them as needed.
I don't think YouTube gives you limitless criteria so you can try following this:
http://www.ampercent.com/youtube-video-search-tips-google-search-operators/8298/
Or try the Filters bar: