I need to update my macbook to os x 10.8

Question

need to update my macbook pro from 10.5.8 to new software for mr iphone 5 and 4 to sync and download new itunes

Answer 1

You only need upgrade to Snow Leopard. Additional information is provided should you decide to upgrade to Lion or Mountain Lion.
Upgrade Paths to Snow Leopard, Lion, and/or Mountain Lion
You can upgrade to Mountain Lion from Lion or directly from Snow Leopard. Mountain Lion can be downloaded from the Mac App Store for $19.99. To access the App Store you must have Snow Leopard 10.6.6 or later installed.
Upgrading to Snow Leopard
You can purchase Snow Leopard through the Apple Store: Mac OS X 10.6 Snow Leopard - Apple Store (U.S.). The price is $19.99 plus tax. You will be sent physical media by mail after placing your order.
After you install Snow Leopard you will have to download and install the Mac OS X 10.6.8 Update Combo v1.1 to update Snow Leopard to 10.6.8 and give you access to the App Store. Access to the App Store enables you to download Mountain Lion if your computer meets the requirements.
     Snow Leopard General Requirements
       1. Mac computer with an Intel processor
       2. 1GB of memory
       3. 5GB of available disk space
       4. DVD drive for installation
       5. Some features require a compatible Internet service provider;
           fees may apply.
       6. Some features require Apple’s iCloud services; fees and
           terms apply.
Upgrading to Lion
If your computer does not meet the requirements to install Mountain Lion, it may still meet the requirements to install Lion.
You can purchase Lion by contacting Customer Service: Contacting Apple for support and service - this includes international calling numbers. The cost is $19.99 (as it was before) plus tax.  It's a download. You will get an email containing a redemption code that you then use at the Mac App Store to download Lion. Save a copy of that installer to your Downloads folder because the installer deletes itself at the end of the installation.
     Lion System Requirements
       1. Mac computer with an Intel Core 2 Duo, Core i3, Core i5, Core i7,
           or Xeon processor
       2. 2GB of memory
       3. OS X v10.6.6 or later (v10.6.8 recommended)
       4. 7GB of available space
       5. Some features require an Apple ID; terms apply.
Upgrading to Mountain Lion
To upgrade to Mountain Lion you must have Snow Leopard 10.6.8 or Lion installed. Purchase and download Mountain Lion from the App Store. Sign in using your Apple ID. Mountain Lion is $19.99 plus tax. The file is quite large, over 4 GBs, so allow some time to download. It would be preferable to use Ethernet because it is nearly four times faster than wireless.
     OS X Mountain Lion - System Requirements
       Macs that can be upgraded to OS X Mountain Lion
         1. iMac (Mid 2007 or newer) - Model Identifier 7,1 or later
         2. MacBook (Late 2008 Aluminum, or Early 2009 or newer) - Model Identifier 5,1 or later
         3. MacBook Pro (Mid/Late 2007 or newer) - Model Identifier 3,1 or later
         4. MacBook Air (Late 2008 or newer) - Model Identifier 2,1 or later
         5. Mac mini (Early 2009 or newer) - Model Identifier 3,1 or later
         6. Mac Pro (Early 2008 or newer) - Model Identifier 3,1 or later
         7. Xserve (Early 2009) - Model Identifier 3,1 or later
To find the model identifier open System Profiler in the Utilities folder. It's displayed in the panel on the right.
     Are my applications compatible?
         See App Compatibility Table - RoaringApps.
     For a complete How-To introduction from Apple see Upgrade to OS X Mountain Lion.