Since you did not describe what you did and didn't do, or how App Store is indicating 5 updates I am not sure how to respond to your question. However, I just downloaded and installed an app with no problem so the App Store is/was working in Texas around 7:00 PM CDT — of course that does not necessarily mean it is working in your area or was working when you checked. (You can always check the system status by going to iCloud.com and click on "System Status" in 7 or 8 point type at the bottom and toward the right of the iCloud window. Both App Store and Apple Online Store have status listings.)

The normal sequence I encounter in Sierra is...
  • A notification appears on the screen from App Store that there are N updates available.
  • At that point I can either dismiss the notification or click on the correct location in the notirication and it will open App Store
  • If I dismissed the notification without opening App Store I can manually launch App Store at any time.
  • In App Store I click on the Updates icon at the lower right end of the app window
  • At that point I can either install the updates one at a time or "Update All"
NOTE: On a few occasions it has taken several seconds for the update window to populate and even longer before the pinwheel stops turning while App Store verifies the available updates.

If we knew what it was we were doing, it wouldn't be called research, would it?

— Albert Einstein