Backup and restore database - occured system error 5
Sounds like a permissions error is being masked. You have to remember that the user that needs access to the folder where the backup resides (and where you restore the backup, if using WITH MOVE explicitly) is the SQL Server service account, not regular users.

If the folder listed in the error message does not represent the same instance where you're trying to restore, it's unlikely the service has access to the folder. Try moving the .bak file to the current instance's data or log folder, where SQL Server will certainly have adequate permissions.