There is no definite numbers to get PR5 or any. Some may get PR5 while having less back links than on PR3 with more back links. I mean, it is not on the quantity, but it is on the quality of the back links...
free directory submission doesn't help much in improving PR, since it is free, most of it do not guarantee inclusion and most are just crap.
yeah, exchanging links can help, but make sure your link is placed on the page where it has PR, also adds do follow on links and having less outbound links, so you can get more "juices."