I thought that upgrading to 6.0 would solve the problem but no!
In the TeamCity Integration menu, I've added a TeamCity Server. I've tested the Connection, it works all very well. The TeamCity Login used is the one for System Admin.
On the same Screen, I click on "You should define mapping between your project and TeamCity build configuration."
When selecting thee TeamCity Project, I'm getting the following error:
"Logic error caused by: GET http://[buildserver]/app/rest/projects returned a response status of 401 Unauthorized"