The database version is "almost" the same (10.2.0.4 to 10.2.0.5) so it pprobably works.But of course, the best option ( the correct one) is to make the upgrade.
¿do you have console access like dba to your database?
In that case, you can do a "startup upgrade "
You can look at <a href="http://docs.oracle.com/cd/B19306_01/server.102/b14238/upgrade.htm#i1011482">Oracle® Database Upgrade Guide 10g Release 2 (10.2)</a>
or you can follow the steps like if you were upgrading the database. The upgrade from 10.2.0.4 to 10.2.0.5 was made by patch 8202632 , you can look at the "README" of this patch and follow the point "11.4.2 Upgrading a Release 10.2 Database" ,