Can my telephone company who has been carrying an outstanding balance for 5 and 1/2 years without a word or notice about collection, now 5 and 1/2 years later demand payment?

Yes of course, they can demand payment 20 years from now. The Statue of limitation only means they can't sue you in court.

They can call and harrass you night and day demanding payment but as
Noted above the sol means they can't sue you in court. It is a debt that you should take care of