How can I purchase AE 5.5 or 6 for my church (non-profit) - (not Creative Cloud)?

CS6 is the only version still available for purchase outright. You can get it by contacting Adobe. Info here.

HOWEVER, if I were in your position, I would be more inclined to go with the subscription to CC which includes AE versions CS6, CC, CC 2014, CC 2015, and all future versions along with the rest of Adobe's software (including Premiere, Photoshop, Illustrator, SpeedGrade, Audition, InDesign, Dreamweaver, and the rest). Plus the connected functionality of the oft-overlooked mobile apps!

The issue I have with purchasing CS6, is that it's already rather outdated. It isn't officially supported on the latest versions of Windows or Mac OSX.

And, as someone who does a lot of volunteer work at my church, I'm all too familiar with having to use old versions (we still use ProPresenter 3 at my church!) Please don't put yourselves in that same boat right off the bat. Join Jesus and Peter and step out of the boat!

Jokes aside, I'm thinking about the cost as well as the functionality. Unless they've discounted CS6 a lot, it would take you a few years of paying the subscription for CC to get close to how much it would cost you to buy the old version of the software (and by then it would have been really outdated!)

But, if you want to buy the old version, the link I gave you should have a phone number to call (I'm pretty sure it's different for whatever country you're from when you go to the page).