Which "Lightroom" did you install? There are two current versions, one is Lightroom Classic which DOES support a second window, the other is the cloud-centric app called simply Lightroom which does NOT support a second window.
"Lightroom version: 5.5" is the cloud-centric version which does not support a second window.
Are you sure it was your intention to use Lightroom (which stores your images in the Adobe cloud), or were you looking to install the Lightroom Classic version, which uses images stored on local hard drive(s) and which also supports a second window (among many other features that Lightroom does not have yet)?
Which subscription plan have you subscribed to? There are two different basic subscription plans:
1. The Lightroom plan with 1TB of cloud space. Includes Lightroom and Lightroom Mobile (on any supported phones or tablets), plus that 1TB of cloud space.
2. The Photography Plan: includes Lightroom Classic, Lightroom, Photoshop, Lightroom Mobile, but only 20GB of cloud space.
If you have the Photography Plan, open the Creative Cloud desktop app and you should see Lightroom Classic as an install option. But if you have the Lightroom-only plan, and you want to switch to the Photography Plan, you will need to contact Adobe's Customer Care team to get the change of plan made.