I'm in the same boat as pirahnya.
I had 4.8 installed on my brother's computer. Upgraded to 5. Had issues with registering, but figured I'd deal with it later.
The trial period expired today, tried all four buttons (Registster now, Insert avast! Pro..., Registration form, Insert the license key) and only the "avast! Pro" button did anything but lock up the interface, and all it did was open a web page with an option to buy the program. I had to use task manager to kill the UI task, tried rebooting a few times. No dice.
I uninstalled avast 5, rebooted, reinstalled avast. I have a fresh 30 day trial period, but I am still unable to register the product. The behavior is the same. I DO see some window flash up and immediately disappear, but it's too fast for my eyes. I suspect (as a developer) that it is a modal window that is behind the avast UI window and won't let me click in it...
Testing... I can hit "ESC" and the avast UI becomes active again.
NEWS! Oh my, I got it to work... Avast, this is a bug.
The registration window comes up NOT VISIBLE! If this isn't a bug, then there is some malware out there hiding your registration windows...
I have a registration key that was emailed to me offline, which I copied to my clipboard. I clicked "Insert the license key" and the interface ghosted a little. Without a visible registration window, I hit Ctrl-V to paste the license key, hit TAB to move to the "OK" button, and hit the space bar. It registered!
Also, before that, I tried to register and found that clicking around the window resulted in things like a drop down list for countries appearing apparently out of nowhere.