Well, first there is no such thing as SQL Server 1997. There is SQL 7 and SQL 2000.
Assuming that your SQL Server is one of those, yes you can simply restore the database backups to SQL Server 2005. Or you can detach the database and attach it to the newer version.
You’ll need to export the logins, jobs, DTS packages, etc that need to be moved so they can be moved into the new instance.