I thought that when I get a page rank, my website would appear on Google's first 5 pages . I also notice that there's another website who's page rank is lower than mine, but it's located on Google's first 2 pages search result. is this possible?

Google PageRank and Search Engine Position at Google are not the same thing.

The PageRank of a website is not related to search engine position in regards keyword targeting.

Optimizing a website to increase PageRank require different methods compared to optimizing a website for good search engine position at Google.

Probably google will consider the back links and the indexing and web design I mean on page meta tags and keywords moreover,is it possible to come in to the result page and thanks for sharing your thoughts..

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The PageRank Search tool allows you to search Google using any keyword(s) you wish. It will then return, in order of Google relevance, the sites associated with those keywords. Each result displays a graphical bar with the PageRank of that particular site.

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