Manifests are usually kept for 2 years as a rule of thumb although some may keep them longer.
As someone that has worked within commercial aviation for some years the EU261 stuff really bugs me. Why compensation is not a percentage of a ticket rather than a flat rate is beyond me.
However given your flight was 5 years ago and no doubt you have moved on with your life do you really have to claim? It is no wonder airlines struggle to make money now a days.....