Download Time Machine for OS X 10.5.8

I recently purchased a new 2015 Macbook Air, and I'm trying to transfer all my data from my old 2008 Macbook Pro. The software on the old Macbook Pro is so out of date that I'm unable to do anything, and all my transfer attempts have been unsuccessful. Also, I was receiving an error using Time Machine about a year ago, so I deleted it (a mistake) and now I want to re-download it. I've searched and been unable to find anything, however, I did find a Time Machine update for 10.5.2, but sure enough, I try to download that and it tells me I need 10.5.2 or newer to download it. I have 10.5.8. That is newer. What am I missing here?

Thanks for any help!