First, let me say that websites aren’t assigned PR, web pages are. So a website’s home page may have high PR but you could be competing with an internal page that has very little PR.
Secondly, search engine results aren’t ranked by PR, they are ranked by relevance. Don’t let the PR intimidate you, there are numerous PR0 pages that outrank PR5, PR6, PR7 and PR8 pages. Ignore the PR and take a closer look at the pages for relevance signals. All that PR doesn’t help if none of the backlinks are relevant. SOC is not determined by PR, it is determined by total relevancy scores.