Which exact version of 11g ? There should be no impact on the Oracle database, as long as all of the pre-reqs for Oracle are included in the OS. You will have to relink Oracle binaries after the OS upgrade
Is It Necessary To Relink Oracle Following OS Upgrade? (Doc ID 444595.1)
Achieving the goal will require some answers to question like
- how much down time is available,
- backup plan if the upgrade fails and etc.
I suggest you perform the action in a TEST bed, document all the steps and corrections taken place during this process if any. Re-implement the process until a successful one shot upgrade is performed then migrate the solution to Production.
RHEL 5.4 and 5.8 does not carries much differences when speaking on Oracle terms, Prepare the OS by setting up the per-requisites and perform the migration.
Having the same mount (identical directory spacing) will help you for an easy migration if downtime is possible. Study the available alternatives, as there are lot to look for from Internet.
Hope this helps!