Updating Lightroom 5 to current Version

Yes, if you subscribe to the Photography Plan, your current work (in your current catalog) will indeed be copied and upgraded to work in Lightroom Classic, which is what you want. You also get the cloud version called Lightroom, which you may or may not want, I have never installed it. Don't confuse Lightroom Classic with Lightroom, even though the names are confusing.

Depends what you mean by the "most current Verison of Light Room"!

The current version that upgrades with the features of Lr-5 (and more added) is called Lightroom-CLASSIC and is at v9.2

Lr-Classic is only available by subscription to the Photography Plan 20Gb.

After installing Lr-Classic by using the Adobe Creative Cloud Desktop App, Lr-Classic will do a copy and upgrade your Lr5 working catalog to be compatible with Lr-Classic 9.2.

OTOH- Lightroom (Cloud based) v3.2 is an entirely new program (NOT at upgrade from Lr5) and your photos are stored in Cloud storage.  Lightroom cannot "migrate" your Lr5 catalog to the Cloud unless you first upgrade it (perhaps with a trial of Lr-Cassic), but there certainly is that facility.

https://www.lightroomqueen.com/migrate-from-classic-to-lightroom-cloud/

https://helpx.adobe.com/au/lightroom-cc/using/migrate-to-lightroom-cc.html

Note that the Photography Plan with 20Gb includes both Lightroom AND Lightroom-Classic & Ps.

The Photography Plan with 1Tb is for Lightroom (Cloud) only &Ps.

WHICH LIGHTROOM IS RIGHT FOR YOU

Buy Lightroom Classic 20Gb or 1tB & COMPARE