Thanks for the quick reply, I do have a 64bit machine, here's what Lightroom says under system info in case it's helpful:
Lightroom version: 5.7 
License type: Perpetual
Operating system: Windows 7 Home Premium Edition
Version: 6.1 
Application architecture: x64
System architecture: x64
Logical processor count: 4
Processor speed: 1.8 GHz
Built-in memory: 15828.1 MB
Real memory available to Lightroom: 15828.1 MB
Real memory used by Lightroom: 401.0 MB (2.5%)
Virtual memory used by Lightroom: 375.8 MB
Memory cache size: 460.3 MB
Maximum thread count used by Camera Raw: 4
System DPI setting: 96 DPI
Desktop composition enabled: Yes
Displays: 1) 1366x768
I just noticed the 1024x768 minimum resolution requirement. Since the Y resolution on my laptop is exactly 768, is it possible that that would prevent the upgrade? Would there be any message letting me know, or does the check for updates function just silently fail?
Thanks for the update.
Resolution would not prevent from upgrade.
Look for Adobe Creative cloud application on your machine and check for Lightroom upgrade within it.
Or, you can directly download the program from the link shared by Per since your machine does support it.
Oh interesting -- I'm sure I'm just confused, but isn't the point of the monthly subscription fee that it includes new versions? If I signed up for a new subscription would I be getting 6.x or 5.x? Again I'm in the digital photography plan, it just says that "It includes Lightroom for desktop, mobile and web, plus the latest version of Adobe Photoshop CC..."
Under Your Apps I show Photoshop CC and Illustrator CC. Lightroom is only listed under Find New Apps, though it's definitely installed and licensed my my system. If I click Install next to Lightroom CC (2015), will my existing catalog, collections, etc. be safe? Is that the best approach?
Sorry, my mistake, since you wanted LR6, I assumed you had a standalone version, the CC version is called LR CC 2015.
In that case, just download from the link I gave you.
Lightroom CC2015 is the version 6.x
It is called version 6 for the standalone users and CC2015 for the subscription users
It will be installed as another application on your end in addition to version 5.
Lightroom 5 and CC2015 versions would remain as separate programs and on the first launch of CC2015, you would be prompted to uprade your Lightroom 5 catalog to CC2015 which would preserve all your edits, collections and everything.
Thanks so much, that did the trick!
Glad to know.