Hello.
I have been doing some investigating into this issue. I have found the issue causing the program not to respond. The addon organizer is unable to read the add-ons.cgf. There is 2 entries in the file that are causing the addon manager not to respond.
You will need to go to the folder C:\ProgramData\Lockheed Martin\Prepar3D v5 open the add-ons.cgf file in a text editor and remove the following entries. You will not need these entries if your are not using the developer tools.
[Package.0]
PATH=Development Tools\Visual FX Tool
ACTIVE=true
REQUIRED=false
[Package.1]
PATH=Development Tools\Traffic Toolbox
ACTIVE=true
REQUIRED=false
Remove the above entries and try the addon organizer again. This solved the problem for me.