Could you clarify a bit more about what you mean by "CPU hog". Client side? Server side? Is it mysql?

If you're talking server side, i'd recommend looking at your caching settings. If it's appropriate for your environment I'd recommend enabling page caching from the dashboard. Usually this is a great option to improve page load times and reduce CPU / Database load for sites that don't have tons of dynamic or frequently changing content on them.

To clarify: I have a CC 5.7.4.2 site installed on Godaddy and it has a plenty of memory and a dedicated IP address for the site but I am still running into 80% of my CPU being used by CC5.7 to run what is a very simple site.

I have the caching options enabled. I even went into the htaccess file and enabled gzip and further cache settings there. But It still hits 75% of CPU.

There's is one thing that I think might be causing this but I'm not sure, so let me run it by you and get your opinion:

in the header of several pages of the theme I have a php script installed which loads a custom responsive image into a div. This image is specified in the page attributes. While I can't see in the testing that I've done if this is effecting the page processing, could it be that this dynamic loading of an image is not being cached. Which of course makes database call and an image load when a page is pulled up?

Or could the CPU demands be due to something else?

Thanks for the input.