Use this link to visit your projects page to see if your new website project is connected. If its there click it, and at the bottom of the following page is an assign license interface to add your themes, and add ons to that project.

http://www.concrete5.org/profile/projects/...

Once its assigned to the new websites project page it can be installed in thats sites dashboard under the 'extend concrete5' category use the install button.

If your new site is not connected than use the 'get more add-ons option in the same 'extend concrete5' dashboard category to get an auto prompt to connect.

Ekko
To save any confusion he does mean another "Account" rather than another "Project",
Take a look at this discussion
http://www.concrete5.org/index.php?cID=329045&editmode=...