Forum Moderators: Robert Charlton & goodroi
Your question touches on a number of different (and significant) areas with regards Google rankings. A good place to start will be the Hot Topics [webmasterworld.com] section of this forum (which is always pinned to the top of the Google forum homepage).
From those topics, a few of the most relevant are related to Google data centres [webmasterworld.com], which is the physical reason you see different results - you're site is in 15th place on some sets of Google computers (data centres), and at 5th on others.
Of course, you likely want to know why your site is in different positions on different data centres. That's a trickier question. There are ongoing discussions on the current situation at both Google.com [pubcon.com] and if you're in the UK, there's a specific thread related to Google.co.uk results [pubcon.com]. Again, you can get to both threads via Hot Topics.
If you're new to things, don't be worried if some of those threads seem a bit overwhelming. You're essentially asking a question which goes to the very heart of the matter: what factors cause a site to go up (or down!) in search engine rankings. There's no simple answer to that question these days!
You might find this thread interesting - Is Google Using a Position #6 "Penalty"? [webmasterworld.com] It turned out that Google was adding something new to the algo last Decemeber but it was buggy (confirmed by Matt Cutts.) Our members spotted it before Google knew about it.
But the bug did show that Google has a way to "force" a URL into a specific position. At the same time, various Google reps were talking about "diversity" or "serendipity" in the SERPs - in other words, giving users a chance to find something new in the searches results.
So unstable ranking might be part of that effort, at least in some cases. I have a client who is cycling back and forth between #11 and #6 on their most competitive term. If we get them to stay on the first page for that search, I'll be sure to let everyone know what turned the trick.