Hello there,
Thanks for using Apple Support Communities.
If you would like to sync your iPhone with a Mac, the Mac needs to be running at least OS X 10.6.8, and have iTunes 11.1 or later installed. If your system meets the requirements outlined below, you can purchase OS X 10.6 from the Apple Online Store, allowing you to update iTunes and sync your iPhone.
To install Snow Leopard for the first time, you must have a Mac with:
- An Intel processor
- An internal or external DVD drive, or DVD or CD Sharing
- At least 1 GB of RAM (additional RAM is recommended)
- A built-in display or a display connected to an Apple-supplied video card supported by your computer
- At least 5 GB of disk space available, or 7 GB of disk space if you install the developer tools
System requirements for OS X Lion and Mac OS X v10.6 - Apple Support
Apple - iPhone 5s - Technical Specifications
Mac OS X 10.6 Snow Leopard - Apple Store (U.S.)
Cheers,
Alex H.