It is possible for Non-EU (non US, Australia, Canada, NZ etc) folks to get permit C after completing five years in CH. In the last 4 years a number of our friends have followed our example and got the C permit. Here's what you need to do...
1. When your renewal for B permit is due after completion of the 5th year, just go for it normally.
2.There is no separate application for C permit for non-EU people applying immediately after completing 5 years. In fact there is no application for at all.
3.This comes under a special category called VINTA. Just Google Vinta and you will get the relevant links. All in German but I am sure either you will understand or someone will be able to explain.
4. What is required is an "application" (i.e. a letter) from you explaining how you like CH, how/why you would like to stay here permanently, how you are integrated etc.
Additionally, you also need to submit the following:
4a. a certificate from your Gemeinde stating you have no financial claims on you from anyone (this is issued on a routine basis for about CHF5 to 20)
4b. a character certificate issued by the central authority in Bern (again a routine thing, you can even apply for it through your local post office. They will need your passport. This certificate is called "casiere judiciare" in French. Costs about CHF20) stating you have no criminal record and no criminal cases pending against you and
4c. a certificate showing your language proficiency. There is no need to specify the level. Just the fact that you are learning the language. This can be from either a school or even a private tutor. They don't actually test it (your language skills). They just need a certificate.
5. All this needs to be submitted to your Gemeinde. They pass it on to the Canton which then passes it on to Bern.
6.In Vaud it took about 4-6 months when we applied, but as you can see from this thread it can be a lot quicker now. In the German part we know of friends who have received in 3 weeks.
7. We had completed 8 years before we applied. Based on our example and our advice as above, many friends and colleague based in GVA/Vaud cantons have got it immediately after completing five years
Hope this helps. Good luck!