Attempting to restore SQL Server 2005 database to a SQL Server 2008 R2 instance gives reason: 15105 error
"MSSQL.1" is not the directory for a SQL Server 2008 R2 instance. 

You should verify the directory you are trying to place the database in.  The default data path for a normal installation is: "C:\Program Files\Microsoft SQL Server\MSSQL10_50.MSSQLServer\MSSQL\Data".

Edit

If this is indeed the path of the databases for your SQL Server 2008 R2 instance then you can verify this by running the following query:


SELECT name, physical_name
FROM sys.master_files
WHERE database_id = 1


You should get results similar to this, highlighted the path for my instance:


You can also verify this path through the restore prompt in SSMS, clicking on the "files":

However also noting that the error message  operating system returned the error '5, the 5 normally indicates permissions issue with the service account running the database engine. If the full message was provided you would see something like 


  The operating system returned the error '5(Access is denied)' while attempting 'RestoreContainer::ValidateTargetForCreation'