You cannot apply for specifically a five-year Schengen visa. The length of visa will be decided by the country granting the visa.
When submitting your visa application, you should answer with the details of the trip(s) you are currently planning:
Your "intended departure date" is the date you leave the Schengen Area at the end of your planned trip.
You can request a multiple entry visa if you want, but if your planned trip doesn't require multiple entries you may still be granted a single-entry visa.
Your "duration of intended stay" is the length of your planned trip.
Being able to demonstrate long travel history (especially within the Schengen Area) improves your chances of being given a multi-year, multi-entry visa, but does not guarantee it. Some countries (especially those with highly tourism-based economies) may be more likely to grant long-validity visas than others, although I can't find statistics on that right now.
As a general rule, if you visit the Schengen Area regularly, you can expect to be granted longer visas over time. See this from the EU Visa Code (Article 24, paragraph 2), on granting multiple entry visas:
(a) for a validity period of one year, provided that the applicant has obtained and lawfully used three visas within the previous two years;
(b) for a validity period of two years, provided that the applicant has obtained and lawfully used a previous multiple-entry visa valid for one year within the previous two years;
(c) for a validity period of five years, provided that the applicant has obtained and lawfully used a previous multiple-entry visa valid for two years within the previous three years.
There are further clauses which allow countries to grant somebody a shorter or longer visa for various reasons, so that progression isn't set in stone. But it should be a good guide for expectations.