I built a site a few weeks ago and had it indexed within a week for not a very competitive keyword. My rank would always jump from 7 to 30th and all the way in between depending on the time of the day. So I started building links and I got 2 PR3 and 3 PR1 sites to link back. The next morning, the site disappeared off Google. Now when I type site:mydomainname.com the site appears, however it is unranked for the keywords. Was I punished for building links too quickly? Is it something that usually happens? If so, when can I expect to rank again?
If you only added 5 links it is highly unlikely that you were penalized for building links too quickly. If those websites posted sitewide links that may be another story, especially if those links all used the same link anchor text. Check around page 5 or 6 for your website. It is common to get knocked back to page 5 for link building related penalties.
do not worry, add more contents, and get more back related links, google will give you good position soon.
Your website as you have mentioned is recently registered and launched and so it might take time before you begin seeing any good results, with or without the links.