Will synthetic oil make a difference in my 2003 mustang gt?
Use the 5W20, it's common knowledge that it's more than up to the task when it comes to engine protection, especially since most of engine wear occurs at engine start up, and thinner oil gets circulating faster than thicker oil. There's no reason to use 10w30.
Also using synthetic oil doesn't mean you get to extend OCI (oil change intervals). It just means that you're using a better than required product.