Is there is a solution for importing existing projects from TFS 2005 server to a new TFS 2008 instance? Yes and this solution is without upgrading original TFS 2005 server to 2008.
While installing TFS 2008 on new server, when wizard prompts you to input SQL server instance for storing data, you can point to database containing TFS 2005 data, this would cause the TFS 2008 installation wizard to perform a data upgrade during installation which would allow TFS 2005 database to work properly with 2008.
Please make sure you have properly backed up your existing database prior to installing TFS 2008, this is because during installation procedure it will do some schema changes on existing database that cannot be rolled back. A proper backup will be necessary for recovery of databases incase of failure of installation.