Software to produce plots for very large data sets?
I assume that you mean 5000 observations. R will work, and RStudio will get you to use R with a bit more GUI than the native application. Commercial solutions like Stata -- which has a soft learning curve, in comparison especially to R -- will also work that kind of sample without any difficulty (by statistical standards, 5000 observations is a relatively small dataset).

The learning curve will matter if you want to reach beyond a mere plot; otherwise, a quick look at the documentation for line graphs should suffice (for R, check there and there, for instance). HTH!