Thank you very much for your replies. I’ve moved MySQL to another server. Now it’s much more faster and it’s CPU usage is max 50%.
The problem seems about sorting queries. After replacing ORDER BY news_date to ORDER BY news_id slow queries decreased. As I need to sort queries by date this won’t be an absolute solution. I’m still looking for a batter way.
I use static files based caching for home page. But seems that it’s not enough. I’ll start caching other most used parts of the site starting with query you suggest.