Is iText 5.4.2 open source?

AGPL stands for Affero GPL.

It basically says, when you want to sell a software product that includes iText or use iText in any commercial webservice, than you need to buy a license.

If you do an open source (with an approriate license) or private project, than you are fine and don't need to buy a license.

The short answer is, yes, iText is open source. The long answer is the next paragraph.

The Affero GPL provides some restrictions, which they would be happy to remove, if you buy a license. For example, you must disclose your source code for apps based on iText, but if you do not want to do that, you can buy a commercial license, freeing you from the AGPL.

The last iText version released under a less restrictive license was iText 2.1.7 (java) and 4.1.6 (c#). It was both released under MPL / LGPL. Even though the authors removed it from the sourceforge page you are able to find it in many places in the web (e.g. maven central). Those versions are from 2009 and still do their job fine, if you need the latest pdf features however (newer versions of digital signatures, ...) or experience a bug you may have to use the latest version...

Update: There was an unofficial java version 4.2.0 but you have to build it for yourself.

Update II: There is a fork called 'OpenPDF' which continues based on that version. Today I would use that project.