The last time I checked, Active State free Perl versions are only for current version and
one version earlier (total of 2). I think they want you to buy a business license (which is very expensive) to access older Perl versions.
I am not sure from your post whether or not you were able to use the ppm on the 5.16 version or not?
I do not think that a update from 5.16 directly to the latest version will work. I think you would have to completely uninstall 5.16 and then install a fresh copy of the latest supported AS Perl version.
Important: You can save and restore a profile file. See >ppm help profile. On your 5.16 machine I think you can ">ppm profile save Myprofile". Save that profile file somewhere "safe". After you have latest Perl version running, use its ppm command line to ">ppm profile restore Myprofile". That should install all the packages that you had before on the 5.16 version. Its been a long time since I have done this. I think I had to find and manually install Tk-TableMatrix because it wasn't in the main AS repository. You may not even have an issue like that at all.