i have 10.5.08 how do i snc my new iphone

The iPhone 5 requires iTunes 10.7.

iTunes 10.7 requires an Intel CPU, running Mac OS X 10.6.8 or later.

So you need to upgrade your Mac to OS X "Snow Leopard":

To upgrade from OS X 10.5.8, you must first buy Snow Leopard by calling the phone number in the Apple Online Store: 800-MY-APPLE (in the US). Snow Leopard costs $20, or $30 for a five user license. Do not obtain Snow Leopard from any source other than Apple.

Make sure your system meets Snow Leopard's requirements:

Mac OS X 10.6 "Snow Leopard" System Requirements

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 memory (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