Can anybody suggest me why the page rank of my websites has decreased from PR6 to PR5 according to google latest page rank updates on 6/12/2013?
There were lots of aglo updates Google made during 2013. But PR hasn't been updated for almost a year (since February). So I assume that perhaps your PR dropped as the result of some search engine also change. But you just didn't know that, as Google didn't provide this data. Check backlinks of your site and their anchors, make sure you have unique (not duplicate) valuble content - these can be the main reasons why your PR dropped.
There was a fresh PR export yesterday. If your PR went down it simply mean that you have less links pointing to your site and/or the PR of those links is less than what it was.