Echoing the comments, make sure to escape backslashes in strings.
dates = c("03-19-76", "04/19/76", "04\\19\\76", "05.19.76", "060766")
> dates
[1] "03-19-76" "04/19/76" "04\\19\\76" "05.19.76" "060766"
Now that you've got the dates stored, there's actually a lot of built in functions you can use with dates. Dates even have their own object types! To do so use as.Date. Since you're using nonstandard date formats, you have to tell R how you've formatted them.
> as.Date(dates[1], "%m-%d-%y")
[1] "1976-03-19"
> as.Date(dates[2], "%m/%d/%y")
[1] "1976-04-19"
> as.Date("20\\10\\1999", "%d\\%m\\%Y")
[1] "1999-10-20"
a <- as.Date(dates[1], "%m-%d-%y")
b <- as.Date(dates[2], "%m/%d/%y")
> b - a
Time difference of 31 days
d <- as.numeric(b-a)
> d
[1] 31
> a + d^2
[1] "1978-11-05"
Note that since you're using 2-digit years, you use %y. If you used 4-digit years, you'd use %Y. If you forget, you'll get oddities like this:
> as.Date("03/14/2001", "%m/%d/%y")
[1] "2020-03-14"
> as.Date("03/14/10", "%m/%d/%Y")
[1] "0010-03-14"
dates = c("03-19-76", "04/19/76", "05.19.76", "060766", "04\\07\\13")