## Your original data is already the result of table().
## Here are two versions, one using barchart and one barplot.
tmpc <- textConnection("
Month Core(%) Non_core(%)
1 45 55
2 48 52
3 36 64
4 60 40
5 35 65
")
tmp <- data.matrix(read.table(tmpc, header=TRUE, row.names="Month"))
close(tmpc)
barchart(tmp, horizontal=FALSE)
barplot(t(tmp))