You can buy yourself some time by restoring the RS2005 databases over the top of existing RS2012 RS databases.
When reporting services starts, it check the version of the SSRS database (ReportServer and ReportServerTempdb) and if necessary it will upgrade them to the version appropriate for that version.
So, you might be able to
- install a new instance of SSRS 2012
- backup the encryption keys of the SSRS 2005 instance
- backup the RS2005 databases (Reportserver and reportservertempdb)
- restore the databases over the top of the SSRS 2012 databases
- restore the encryption key in the SSRS 2012 environment
This should give you a working SSRS 2012 instance with all of the reports that are currently in the SSRS 2005 instance
This will completely trash whatever was previously in the SSRS 2012 instance. Hence, the first step is critical.