You need a company to sponsor you to get the clearance. It can either be the perspective employer or a consulting firm looking for contractors for government projects. Just go find one and ask them to sponsor you. If you got the right profile, chances are they will do it for you. You only need to fill in a form with some basic information. You may need to provide some historical info such as where you lived in the past 5 years, duration, reference, etc., but nothing too onerous.
"Enhanced Reliability" is the lowest level of security clearance and the easiest to get, normally can be approved by RCMP (?) within a day or so. I don't think residing in Canada for 5+ years is mandatory as long as the official feels comfortable about the clarity of your experience. I heard some new immigrants got it within 1 or 2 years after arrival. Just give it a try. Good luck!