how do i update safari 5.0.6 to current version?

Apple menu > Software Update.

You appear to be running Mac OS X 10.5.8. Choose About this Mac from the Apple menu and check the processor.

If it's a PowerPC Mac, it's already running the newest OS it can.

If it's a Core Duo Mac, click here, install the DVD, and run Software Update.

If it's a Core 2 Duo or better Mac, upgrade it as if it was a Core Duo Mac, and if desired, open the Mac App Store, and try downloading 10.9. If you get told it's incompatible, go to the online Apple Store and order a download code for Lion 10.7.

Mac OS X 10.7 and newer don't support PowerPC software such as Microsoft Office 2004. If you upgrade the OS, back up the computer first.

It isn’t necessary to upgrade past 10.6.8 to use the current version of iTunes.

(111519)

Betty, note that in the second "If" line of Niel's post, the link there takes you to where to buy OS 10.6--you can't download that. Once bought and installed, then the updates are available for downloading.

Start by checking if you can run Snow Leopard:

Requirements for OS X 10.6 'Snow Leopard'

http://support.apple.com/kb/SP575

(NB: PowerPC applications can still be run in Snow Leopard using Rosetta, but they will not work in later versions of OS X. For detailed information see this user tip: https://discussions.apple.com/docs/DOC-6271 )

The OS 10.6 Snow Leopard install DVD is still available for $19.99 from the Apple Store:

http://store.apple.com/us/product/MC573/mac-os-x-106-snow-leopard

and in the UK:

http://store.apple.com/uk/product/MC573/mac-os-x-106-snow-leopard

Before installation you should back up all your data.

When you have installed it, run Software Update to download and install the latest updates for Snow Leopard to bring it up to 10.6.8, or download the combo update from here:

http://support.apple.com/kb/DL1399

Check via Software Update whether any further updates are required, particularly to iTunes (you will need the latest version in order to synch with mobile devices).

You should now see the App Store icon in iTunes, and you now need to set up your account:

http://support.apple.com/kb/HT4479

You can now upgrade to Mavericks OS 10.9 for free IF you have one of the following Macs, with not less than 2GB of RAM, and at least 8GB of available space on your hard drive:

iMac (Mid-2007 or later)

MacBook (13-inch Aluminum, Late 2008), (13-inch, Early 2009 or later)

MacBook Pro (13-inch, Mid-2009 or later), (15-inch, Mid/Late 2007 or later), (17-inch, Late 2007 or later)

MacBook Air (Late 2008 or later)

Mac Mini (Early 2009 or later)

Mac Pro (Early 2008 or later)

Xserve (Early 2009)

iCloud system requirements:

http://support.apple.com/kb/ht4759

If you cannot run Mavericks you can purchase the code to use to download Lion from the App Store (Lion requires an Intel-based Mac with a Core 2 Duo, i3, i5, i7 or Xeon processor and 2GB of RAM, running the latest version of Snow Leopard):

http://store.apple.com/us/product/D6106Z/A/os-x-lion

or Mountain Lion:

http://store.apple.com/us/product/D6377Z/A/os-x-mountain-lion