This was a little obscure, but, one can find how the SDK is pulled by VEXcode V5 by unpacking the application, and finding the app.nw file (which is just a glorified .zip file). Once you've unzipped it, look for build/server/sdk_updater.js (which, thankfully, hasn't been turned into bytecode, but you could just as easily find it if it was in bytecode).
In this file, you'll find these lines:
URL_PUBLIC is what you're looking for. You'll want to then visit this website: ${URL_PUBLIC}/catalog.txt. That site will have the most recent version number of the SDK to download.
Then, with both URL_PUBLIC and the version number from ${URL_PUBLIC}/catalog.txt, you can proceed to download the VEX V5 SDK at ${URL_PUBLIC}/${VERSION_NUMBER}.sdk. This will download a file ending in a .sdk extension, which is just a .zip file renamed.
Congratulations! You just downloaded the VEX V5 SDK!