yes, you can successfully restore a database backup created on SQL Server 7 to a SQL Server 2005 database server, however, there a couple of things to remember when you do it:
1. The database will restore in Compatibilty mode 7 (you can tell by right-clicking the db, then selecting properties and going to options > Compatibility level) - this means a a couple of things:

A. if your application or the stored procs use the old ∗= syntax for left/right joins your queries will continue to work - that's good
B. you cannot use right click on the database, select Tasks > generate scripts - No database in compatibility mode will appear in the list of databases to script. that's bad - although you could probably still use ErWin to reverse engineer the database into SQL scripts.
So the answer is that you really should change the compatibility mode and fix the legacy syntax in your code (though I personally liked the old syntax better!). What that means is changing queries that may have looked like this:
select deptpermissions.departmentid, block.blockcode, block.blockname from deptpermissions, block
where block.blockcode ∗= deptpermissions.blockcode
and departmentid = &departmentid;
order by block.blockname, deptpermissions.departmentid
to look instead like this:
select deptpermissions.departmentid, block.blockcode, block.blockname from block
LEFT JOIN deptpermissions
ON block.blockcode = deptpermissions.blockcode
where departmentid = &departmentid;
order by block.blockname, deptpermissions.departmentid