How to convert DB2 9.5 to DB2 10.5 online (Linux)
You cannot migrate the database online. 

You can use InfoSphere DR or any other replication software for migration with minimal downtime, however, if your application itself does not support transparent connection failover you will still experience a brief outage. 

The process in brief would look like so:


Install DB2 10.5.
Create a new database in a DB2 10.5 instance, using db2look.
Install and configure replication software.
Perform a full refresh from the old (V9.5) database to the new one.
Continue mirroring until the new database catches up to the old one.
Initiate application failover.
Stop replication once the application has fully failed over.