Well one of my peer from Consulting team had asked this question tried looking for MSDN article but not find any so thought of writing it to my blog:

Question: How to Migrate Database from SQL 2005 to SQL 2008

Scenario 1 - Moving SSAS Databases from SQL 2005 SSAS to another Server where we have SSAS 2008 Services

Procedure:

Backup SQL 2005 DB and restore it on SQL 2008

Open AS Database in BIDS and Fix AMO Warnings
What are these AMO Warnings - in SQL 2008 BIDS Best Practice Rules are embedded in BIDS and if your database design go against these rules you will get warnings in BIDS itself.

or

Import SQL 2005 AS DB in SQL 2008 BIDS Project

Fix AMO warnings and deploy that db on SQL 2008 Server
Caveat - In this approach you need to fully process the database so I recommend to go for Backup and Restore.

Scenario 2 - Upgrading SQL 2005 to SQL 2008

This Article talks about it:

How to: Upgrade to SQL Server 2008

Considerations for Side-by-Side Instances of SQL Server 2008 R2 and SQL Server 2008