Does the same happen if you try to register from one of the other TCS products (e.g. FrameMaker or Captivate)?
Issue Update: This issue resolved through our IT Department and Adobe.
On a related note: After licensing Technical Communication Suite 5 I received the "Thank You" window from Adobe.
Unfortunately, the wording in their "Thank You" window didn't match the actual product version licensed (see attached image).
This is the fifth QA mistake I've noted in just two days of using the product. Come on, Adobe. You can do better than this.