Given the data in your example:
> m <- data.frame(YEAR=c("/1931", "/1924"),RECENT=c("09/08/2005","11/08/2005"))
> m
YEAR RECENT
1 /1931 09/08/2005
2 /1924 11/08/2005
Extract year with the strptime function:
> strptime(m[,2], format = "%m/%d/%Y")$year - strptime(m[,1], format = "/%Y")$year
[1] 74 81