I am having nothing but problems trying to upgrade firefox on my FC3 system to 1.5 and install the flash plugin. Man, Windows and IE were never nearly this much of a headache!
First of all to install 1.5 I had to extract from the tarball into a folder called firefox. However the version that installed when I installed FC3 is in a foder called .mozilla. so I just moved the firefox folder to mozilla to try to replace the old software, there is no option to do this automatically when you install firefox 1.5.
When I try to install the flash plugin, the installer always insists on installing it in .mozilla and doesn't give me an option to change the path like Windows installer always does. Furthermore you are supposed to be able to install manually, according to the instructions on the website, by moving the files flashplayer.xpt and libflachplayer.so into the plugins directory. I have moved those to files into the plugin directories under both ./.mozilla and ./.mozilla/firefox, but when I try to get to websites that use flash, the plugins still don't work. It's just like they are not even there. IE under windows updates and installs plugins in seconds, I've been working on trying to the same task for firefox under linux for a couple of hours! And I have a fair amount of experience with Unix systems.

first, the .mozilla folder is where your user profile files for the browser reside.

2. Fedora comes with firefox installed in /usr/lib/firefox-1.x.x.x
you can leave it there( the old one) or remove it with
rpm -e firefox

3. You should place the firefox 1.5 folder (from the firefox-mozilla site) in /usr/local/

4. Install the plugin files in /usr/local/firefox/plugins

5. On your desktop you can edit the web browser link properties or create a new link execute
/usr/local/firefox/firefox

Good Luck.