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.