I know everyone's going to say 'it depends' and 'its hard to say' and all that, but out of PERSONAL EXPERIENCE, are 3 PR5 Links with relevant anchor text enough to get a Pagerank 1, 2 or even a 3? Soroush King,
Whats the keyword? how much links were there on the pages that you are linked? whats the anchor? how good is the page optimized? ET CETERA! There are too many factors. So 'its hard to say' and 'it depends'. Out of personal guess: I'd say NO. But its very important what kind of keyword you are after. If its HGADFDFADHGDWREEEE then I say yes
I know you don't want this answer, but there is no way to tell. Anchor text doesn't matter. PageRank is only about backlinks to your site. A PR5 site can pass about 85% of its PR but that is divided among the number of outgoing links on the page. If the page has 30 outgoing links, it isn't going to pass much PR. If there are only a few outgoing links, you could even get a PR5. The PR5 page(s) linking to you could be a 5.01 or 5.99 and you have no way of knowing which. I've found a PR3 and PR4 pretty easy to get. A PR5 requires some work. A PR6 requires a lot more links - it's approximately six times as hard as a PR5. Without knowing how many outgoing links the page has, I would throw out a guess of a PR2 or PR3- with an outside chance of PR4. Instead of focusing on PR, just keep building relevant backlinks if you want to rank well for a competitive keyword. 3 PR5 links isn't going to be nearly enough. Google uses internal PR for SERPS and that is updated several times a month. You will get the benefit of the links before you see PR on the toolbar - unless you domain is new. Google will sandbox most new domains for at least 3-4 months and not use/factor in your backlinks until you are released from the sandbox. The sandbox doesn't affect your PR from showing on the toolbar when it updates (about every 3 months).
As you know there are a billion and one other factors, but from personal experience I would say yes it is possible to get a PR3 from 3 PR5 links and maybe even a PR4 Strange question to ask though as PR is not that important it's the position in SERPs that you should be working on.
Here is an article about calculating page rank: http://www.compar.com/infopool/articles/PR-calculation.html I've no idea how close to the mark it is though...
Thanks spondishy for that link, its fantastic. and thanks everyone else for their help too. Soroush King,