No, you can't use Avery label 5390 Name Tag. I have checked The Print Shop's website, and there was nothing related to this element. Other websites of the same category offer the same vague information about supported elements. On the official website, there is a comparison chart where you can see the supported features of two versions. The Avery element is not mentioned anywhere. These apps offer a pre-defined database. If it's not there, then it's not supported.
Check the comparison list using the following page: http://broderbund.com/p-721-the-print-shop-deluxe-35.aspx