I would like to create a 5 question feedback survey with a 4 point rating scale.

Can I create a calculation that will give me an average score?

Yes, you can perform calculation using the Form Calculation widget, please check this guide: http://www.jotform.com/help/259-How-to-perform-calculation-in-the-form

Example:

Result: https://form.jotform.co/60367056432857

Let us know if you need more help, we will be glad to assist you.