First of all, you need skype 7.36 (Keep in mind this is not the latest skype, but the last 7.xx version to be supported.)
And then, download skype 5.5 if you don’t have it already: https://drive.google.com/file/d/0B0QZbkUatQzsY1hjSmtDeFJpVHc/view?usp=sharing
Starting off, Open Skype 7.36 and login to your microsoft account. After logging in, you don’t need to do anything in 7.36, just quit it (Don’t log-off)
Now, go to your Appdata Roaming folder, in case, the skype folder inside of it (most likely localized in C:\Users<yourusername>\AppData\Roaming\Skype). You can also open it by typing in your search bar in the start menu for %appdata% and then going to the skype folder
Delete these 2 files:
This is absolutely necessary for it to work, if you don’t delete those, skype 5.5 will log you off right in the start and you will have to do it right from the start (in this case, logging into 7.36)
Now, open Skype 5.5, and you should be logged in
Observation: You can’t add contacts on skype 5.5, to do so, add them by your phone or by skype 7.36, im not sure of this.