Is there a way to upgrade WebSphere 8.5.5.10 to version 9?
When installing Fix Packs using IBM Installation Manager, I only add the repository.config, but after adding the repository.config for Version 9, I only have the install option.
You'll have to do a new install of v9, and then migrate your configuration from the old to the new environment. There are a few different kinds of config migration, but the main overview is here: https://www.ibm.com/support/knowledgecenter/SSEQTP_9.0.5/com.ibm.websphere.migration.base.doc/ae/welcome_migrating.html
In particular, the provided tools will include WASPreUpgrade (https://www.ibm.com/support/knowledgecenter/en/SSAW57_9.0.5/com.ibm.websphere.migration.nd.doc/ae/rmig_WASPreUpgrade.html) and WASPostUpgrade (http://www.ibm.com/support/knowledgecenter/en/SSAW57_9.0.5/com.ibm.websphere.nd.multiplatform.doc/ae/rmig_WASPostUpgrade.html). For each profile you want to migrate, you use WASPreUpgrade to create a backup of your old configuration in a separate location, and WASPostUpgrade to merge that configuration with a new profile in the new configuration. You can do this disabling the old environment (standard migration) or keeping them both running side by side (clone migration) and have a choice of staying on the same system or migrating to a new one (remote migration.) All those terms are explained in the overview.