How to Restore SQL Server 2008 Backup in SQL Server 2005

Is it possible to restore Sql Server 2008 backup in sql server 2005

No. It is not possible to restore a database from a backup of a newer version.

If you are dead set on it, I think your best option is to selet the database in the Object Explorer in SQL 2008,
right-click, select Tasks->Generate Scripts.In the options dialog emable about everything, including Script Data.

And make sure you select "Script for SQL 2005".

Source

When importing the objects into your target server, if the objects are large you may find that you can't open the SQL file via Management Studio (with a completely useless "The operation could not be completed" error, no less). That's okay, just load the file via sqlcmd.

How to migrate a database from SQL Server 2005 to 2008 as is?

Just RESTORE it on the SQL2008 server and it will be automatically upgraded. And you can check if you're a sysadmin using IS_SRVROLEMEMBER.

backup sql server 2008 and restore to sql server 2005

From a technical point of view, you can definitely install two instances of SQL Server (even different versions) on a single machine:

Install SQL Server 2008 as default instance and access it as (local)
Install SQL Server 2005 as SQL2005 instance and access it as (local)\SQL2005

Either do this, or get a second machine (physical or virtual)

Can I restore a SQL Server 2005 backup on SQL Server 2008?

Yes. MS-SQL is backward compatible.
Just try.... :)

How can I get a SQL Server 2005 compatible backup from SQL Server 2008 database?

Unfortunately, SQL Server has never supported this - and still doesn't :-(

There is no way you can create a backup in a newer version and restore it in a previous version - and this goes from SQL Server 4.2 all the way through 2008 R2.

All you can do is either create scripts and run them on the target server, or use tools like SQL Compare and SQL Data Compare to compare the two databases and update the target database from the source (basically, what these tools do is create and execute the necessary scripts in the background, so you won't have to fiddle and create those scripts yourself)

Move database from sql server 2008 to 2005

I don't think you can restore 2008 backup on 2005 server. Try 3rd party schema/data migration tool, like SQL Examiner Suite or RedGate's SQL Compare