I don't believe that Adobe is offering a subscription currently to Creative Suite 5. That is a very old product. Your link or information is out-of-date.
You need to buy a subscription for the Adobe Creative Cloud:
Wasn't there a subscription to Connect, or to a stock photo service (I know there was the stock photos at some point, and it was discontinued a year or so later)?
That was CS3 or maybe even earlier. I'd like to see a screenshot of that alert.