You say you have restored the SQL 2005 ReportServer db and ReportServerTempdb to your SQL 2008 R2 system and are using those with the SQL 2008 R2 binaries.
If so, I do not think you have a system that will be supportable by Microsoft. You need to use the SQL 2008 R2 report server databases with SQL 2008 R2.
Original author: https://github.com/SQL-FineBuild/Common/wiki/ 1-click install and best practice configuration of SQL Server 2019, 2017 2016, 2014, 2012, 2008 R2, 2008 and 2005.
When I give food to the poor they call me a saint. When I ask why they are poor they call me a communist - Archbishop Hélder Câmara