Greetings mshields61xx,
Thanks for visiting Apple Support Communities.
It sounds like you want to sync your iPhone 5s with your Mac Mini instead of the PC you currently sync with, and you want to make sure not to lose data. This can be done, although there are several steps in the process.
You can use the steps in How to move your iTunes library to a new computer to copy the contents of your iTunes library to your Mac Mini. These steps will help prevent loss of the music you've imported from CD. Once you've completed the steps in this article, you'll need to sync your music from the Mac Mini to the iPhone again.
If you no longer intent to use iTunes on the PC, you can deauthorize it by choosing Store > Deauthorize This Computer from the iTunes menu bar.
For songs you've purchased from the iTunes Store, you can transfer purchases from your iPhone to the Mac, or try to download them from the iTunes Store again:
How to transfer data from a PC to a Mac - Apple Support
Download past purchases - Apple Support
Best Regards,
Jeremy
