The name for such a badge doesn't have to convey "5 years"; the duration is just a criterion, as is the points threshold.
I think a better name is "Veteran", which would look like:
"Veteran" better conveys the meaning and significance of the achievement, without necessarily conveying the quanta used to determine it.
Regarding the points requirement, consider at least 1K (maybe 2K) in a year to make that year count towards the badge, rather than an average per year which could lead to people briefly using a old, even dormant, account to crank out 1K in a couple of weeks to game the badge.