I have Mac OS X 10.5.8 (9L31a) installed, should I upgrade to Yosemite?

Impossible to say.

Do you need Yosemite?

Can your current computer support the upgrade?

Do you have apps that need Yosemite to run?

Do you have any Apps that may not run on Yosemite?

You may want to read here:

https://www.apple.com/osx/how-to-upgrade/

With that said, you won't be able to update directly from 10.5.8 to Yosemite, you'll need to update to at least 10.6.8 before going to Yosemite. 10.6 Snow Leopard is $19.99 from the Apple Store.

http://store.apple.com/us/product/MC573Z/A/mac-os-x-106-snow-leopard

Apart from 'should you', also ask yourself 'can you'?

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

and then to Yosemity is you can run it.

Before embarking on a major OS upgrade, it would be wise, advisable and very prudent if you backup your current system to an external connected and Mac formatted Flash drive OR externally connected USB, Thunderbolt or FireWire 800, Mac formatted hard drive. Then, use either OS X Time Machine app to backup your entire system to the external drive OR purchase, install and use a data cloning app, like CarbonCopyCloner or SuperDuper, to make an exact and bootable copy (clone) of your entire Mac's internal hard drive. This step is really needed in case something goes wrong with the install of the new OS or you simply do not like the new OS, you have a very easy way/procedure to return your Mac to its former working state.

Then, determine if your Mac meets ALL minimum system install requirements.

Mac OS X v10.6 Snow Leopard system requirements

Purchased Installer disc here

http://store.apple.com/us/product/MC573Z/A/mac-os-x-106-snow-leopard

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.

OS X 10.7 Lion system requirements

Purchased emailed download code here.

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

To use OS X 10.7 Lion, make sure your computer has the following:

An Intel Core 2 Duo, Core i3, Core i5, Core i7, or Xeon processor

Mac OS X v10.6.6 or later to install via the Mac App Store (v10.6.8 recommended)

7 GB of available disk space

2 GB of RAM

To install OS X 10.8 Mountain Lion, 10.9 Mavericks (free upgrade, but currently unavailable) or OS X 10.10 Yosemite (currently available free upgrade) you need one of these Macs:

OS X 10.8 Mountain Lion purchased emailed download code here.

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

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),

MacBook Pro (15-inch or 17-inch, Mid/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)

Your Mac also needs:

OS X Mountain Lion, Lion, or Snow Leopard v10.6.8 already installed

2 GB or more of memory (I strongly advise, at least, 4 GBs of RAM or more)

8 GB or more of available space

Next,

If you run any older Mac software from the earlier PowerPC Macs, then none of this software will work with the newer OS X versions (10.7 and onward). OS X Snow Leopard had a magical and invisible PowerPC emulation application, called Rosetta, that worked seamlessly in the background that still allowed older PowerPC coded software to still operate in a Intel CPU Mac.

The use of Rosetta ended with OS X Snow Leopard as the Rosetta application was licensed to Apple, from a software company called Transitive, which got bought out, I believe, by IBM and Appe could no longer secure their rights to continue to use Rosetta in later versions of OS X.

So, you would need to check to see if you have software on your Mac that maybe older than, say, 2006 or older.

Also, check for app compatibilty here.

http://roaringapps.com/

If you have any commercial antivirus installed and/or hard drive cleaning apps installed on your Mac, like MacKeeper, CleanMyMac, TuneUpMyMac, MacCleanse, etc. now would be a good time to completely uninstall these apps by doing a Google search to learn how to properly uninstall these types of apps.

These types of apps will only cause your Mac issues later after the install of the new OS X version and you will have to completely uninstall these types of apps later.

Once you have determined all of this, you should be able to find the latest versions of OS X by clicking on the Mac App Store icon in the OS X Dock and then login to the Mac App Store using your Apple ID and password and if you purchased a download code, input that code.

You can then begin the download and installation process of installing the newer versions of OS X from the Mac App Store.

Good Luck!