I do hope those are offline backups for LUW, as you can't use online backups to restore to later versions. You also can't roll-forward logs through Db2 versions, as I'm sure you know.
You also have fixpacks and changes between versions that may affect your ability to restore - 10.5 log and lsn changes come to mind.
Anything older than 11.1 has to be restored/upgraded to Db2 10.5 Fix Pack 7 or later first, then upgraded to the later version. (11.5 and 12.1 say the same thing) https://www.ibm.com/docs/en/db2/11.1.0?topic=servers-recovering-through-db2-server-upgrade
I had to ponder this issue a few years back for a financial institute. My thoughts then were that you would need to archive the matching Db2 installation media alongside those backups, or you may well struggle with the restores. Also whatever build info applied to the servers and/or database installations. Other problems then arise in that you need a compatible OS for the Db2 installation, compatible hardware etc. You may be able to get around that with VM images, but it will be messy. If it is just the data that needs to be retained for 35 years, then export to CSV, compress and store with the DDL for the tables. Db2 backups from older versions are going to be tedious if you need to retrieve them 10+ years from now. Not to mention all the security holes from using old versions.
Short answer - 10 years, maybe, but with effort. More than that you may very well need your friendly neighbourhood IBM support to help out with installation images etc.
Cheers
------------------------------
Greg Palgrave
------------------------------