Spoiler - though they were both G5 storms, they weren’t really that comparable.
Also, big as the Carrington Event was, it’s likely it was absolutely dwarfed by one about a millennium ago, the Miyake Event
How do we know there was a storm a millennium ago, and even its measurements?
See Miyake event.
Trees!
Trees store lots of environmental and atmospheric data in their trunks. When they get fossilized a lot of that information remains intact.
Also, ice cores. Layers of ice protect previous layers of ice from further contamination, so are a pretty good snapshot of the environment/atmosphere at a given point in time.https://www.bbc.co.uk/newsround/67074940
Wiki has more detailed information on how Miyake Events are “stored” in trees and ice cores.
https://en.m.wikipedia.org/wiki/Miyake_eventThank you!
As with any fossils, through the study of radioactive isotopes such as C-14.