As said, these are two independent applications. No need to uninstall it. Actually if you are song HALion One in your projects, make sure you keep it installed on your system.
I believe the 9 license can be installed on all versions of the eLicenser. There’s quite a useful article here from which you might be able to work out which version you have…
The only thing that may be of concern is where it says: "When using a 1st generation USB-eLicenser, the graphical user interface of licensed software may feel less responsive. In this case, we recommend replacing the USB-eLicenser with the latest model." I think Studio 5 is more recent than this, however, but checking against when you bought it or the product timeline might confirm this.
Moving licenses from an old licenser to a new one is not complicate, I did it myself last year after my old one started feeling a bit ropey (physically falling apart).