Hi Andy. Reading through your post, it seems like you are generally on the right track for doing the upgrades. I recommend taking a look at this topic in the IBM Documentation for Spectrum Control that covers a DB2 upgrade from 10.5 to 11.5.
Example of upgrading Db2 in a Windows environment
https://www.ibm.com/docs/en/spectrum-control/5.4.2?topic=migrating-example-upgrading-db2-in-windows-environmentStep 5 to take the backup is key to having the data to recover if anything were to go wrong. If your system is a VM, a snapshot is also an option to quickly restore a prior environment. Before you begin, it is also important to make sure your Windows operating system is one supported with DB2 11.5.
DB2 support for Spectrum Control + links to IBM Documentation for DB2 - https://www.ibm.com/support/pages/node/6249433Operating system support for Spectrum Control - https://www.ibm.com/support/pages/node/6249419#swindows
If you have problems with the installation of DB2 or Spectrum Control, please reach out to IBM Support by opening a case.