If you can't find a better solution, you could manually modify the scale like in this example.
Note: Please make your questions providing a REPRoducible EXample (reprex) like the one below.
library(tidyverse)
set.seed(1)
df <- data.frame(year = seq(1950, 2010, 10),
value = rnorm(7))
df %>%
ggplot(aes(year, value)) +
geom_line() +
scale_x_continuous(breaks = seq(1950, 2010, 10),
labels =str_replace(as.character(df$year), "^\\d{2}(?!(5|0))", "'")) +
theme_minimal()
Created on 2019-09-12 by the reprex package (v0.3.0.9000)