Wordpress site really slow due to high CPU usage

One of my Wordpress websites is incredibly slow both front end and in the dashboard. I have deleted plugins, deactivated the ones I want to keep, changed the theme 3 times but this has not helped. Now the host says that the index.php file is using 35.5% - 38% of CPU. I have looked into this problem that seems to be a common WP fault but there seems to be so may variables. I am looking for someone who has experienced and fixed this problem before please.
Thank you.