Do you need different set of user to test different platform of a product?

I am assigned to do usability test from a new bookstore website in mobile and desktop. Because of the limited resources, I need to be careful in recruiting participants to get the best result.

So I need to be sure: - Do I need to use different set of user (ex. 5 user for website in desktop and 5 user for mobile) or i can use the same set of user (ex. 5 user test both platform) - What is the pros and cons of using the same set of user to test a different platform of a product?