As you probably know, Joomla 1.5 has reached end-of-life. It's no longer supported, and you shouldn't use it. OK?
That said - there are situations where the use of Joomla 1.5 is inevitable. For instance, I regularly come across people who want me to help them port their site to the latest version of Joomla. Sometimes, the site can't be upgraded immediately. Perhaps there's a financial issue at hand. Other times, it can be that the site is so complex and full of outdated extensions and special solutions that it's not possible to migrate without building new components or find alternatives. This can take time, and while you find the solutions the site needs to stay secure.
Often, the site has been neglected for a while. It might be on Joomla 1.5.15 or another old version. It might also be full of extensions that indeed have been updated by the devloper, but has not been installed on the site. This means that I will have to install the latest versions of any updated extensions for Joomla 1.5. I do this primarily to secure the site as much as I can while finding an upgrade path that will work for the client.
So, where do you find extensions that are compatible with Joomla 1.5? Enter archive.extensions.joomla.org.
This site is a listing of extensions for Joomla 1.5, complete with a warning from the JED, that these are for an outdated version of Joomla. On the site, you can browse and search for Joomla 1.5 extensions.
That said, you shouldn't use 1.5. OK?