Your Skype ID can have one of the two formats:
live:cmdmember
live:.cid.5231ef07ed4acb6f
Either way, your Skype ID will be valid. Make sure to correctly copy it!
Finding your Skype ID is very easy, and it takes 30 seconds.
Log into your Skype account, click on your Skype picture and then on the "Skype profile" button. A new window will pop up.
Scroll down a little, and you will see your Skype ID at "Skype Name".