10.5 is not longer sold by Apple. It is not downloadable. You can look for a retail copy on eBay or Amazon. If you have an Intel Mac, then you may be able to upgrade to Snow Leopard or higher.
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
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.
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?
For a complete How-To introduction from Apple see Upgrade to OS X Mountain Lion.
I have a Mac OS X 10.4.1, with the following Hardware, Model Identifier found in the System Profiler in the Utilities Folder. Can my OS still be upgraded?
Model Name: iMac
Model Identifier: iMac5,1
Processor Name: Intel Core 2 Duo
Processor Speed: 2 GHz
Number Of Processors: 1
Total Number Of Cores: 2
L2 Cache (per processor): 4 MB
Memory: 1 GB
Bus Speed: 667 MHz
Boot ROM Version: IM51.0090.B09
SMC Version: 1.8f2
You can upgrade to Snow Leopard as is. To upgrade to Lion you need to add more RAM. I would add more RAM anyway but only upgrade to Snow Leopard by purchasing the DVD. Information is in my earlier post.
If you decide to upgrade RAM then check OWC or DataMem to find the memory needed for your particular model. Your computer requires memory in pairs, so you would replace the pair you have with a new pair. For example, two 1 GB modules will give you 2 GBs of RAM. Your computer can be expanded to two 2 GB modules for a total of 4 GBs. However, due to the hardware you will only have 3 GBs usable.
Maximum Memory 3.0 GB (4.0 GB can be installed, only 3.0 GB will be addressed) Memory Slots 2 - 200-pin PC2-5300 (667MHz) DDR2 SO-DIMM