You need to reactivate after downloading.
Purchasing Sphere is at the website level, you still need to activate it on your local machine.
Once you've reinstalled Studio One, open the program, go to Studio One in the menu bar, select Activation, the window that pops up will have "Activate with Sphere" already selected, click the green button where it says "Activate" and then you'll get a notification that your Sphere License is activated on that installation of Studio One.
Close Studio One and relaunch it and it should be Studio One Pro.
If for some reason it doesn't say Professional, download the installer for Studio One 5 Pro from your my.presonus.com account again, and run it, it will install over your existing installation. Your data is safe in your My Documents (windows) / Documents (Mac OS X) folders. When you launch Studio One again, it will say Professional and in the start up routing you'll see "Activated with Sphere License".