Unless you have an image system/server in place already, upgrading from OS 10.5 to 10.10 can be a pain. There are several reasons why.
Back in the day of OS 10.5, there was was no Mac App Store only iOS app store
Mac operating systems were only available on DVD
- OS 10.6 is not available in the app store
So, In order to upgrade from 10.5 to the current OS version you have to upgrade to 10.6 first. You can not jump from 10.5 to 10.10 for a couple reasons. Just make sure you install all 10.6 system updates which will stop at 10.6.8. Then you can access the AppStore and jump to 10.10 Yosemite.
If you do not already have a DVD copy of 10.6, you will need to purchase 10.6 snow leopard from this link from apple: http://store.apple.com/us/product/MC573Z/A/mac-os-x-106-snow-leopard. At least this is the "legit" way of doing this :) Apple only has 10.6 available to ship to you on DVD. It is not available through the App Store. But just think, this is the last OS you will need to pay for...at least for right now.
If for some reason you don't want to upgrade all the way to 10.10 Then if you want to upgrade to 10.7 lion, You have to call 1-800-800-2775 for education purchasing. They will give you a redemption code that you can use to download lion from within the App store. This is because apple only keeps the most current OS available in the AppStore