First of all, if you haven't already done so, ugrade to the latest kernel, at present 2.6.18-194.17.4.el5 .
First you will have to add the EPEL repository because when getting the relevant broadcom packages they rely on this to be enabled for dependency resolution.
EPEL provides add-on packages for Red Hat Enterprise Linux 5.x and 4.x releases and compatible derivatives (and also for 6.x in view of the upcoming release). EPEL packages are in most cases built or derived from the equivalent ones in Fedora repository and maintained by the same people. You can read more about the whole project here to find out more about the quality of packages etc, or just skip ahead to add the repository.
Currently, what you want is this command:
su -c 'rpm -Uvh http://download.fedora.redhat.com/pub/epel/5/i386/epel-release-5-4.noarch.rpm'
Enter it into a terminal and hit enter. Yes, epel-release-5-4 is correct, there is no 5.5 yet.
Then in Yum Extender or whatever your package manager of choice in Scientific Linux you should already have the Atrpms repository listed. Enable it and the EPEL one and refresh the package listing. Make sure you're looking at available packages through the filter, not updates or installed. Search for broadcom and the correct packages available for your architecture should show up.
Choose broadcom-wl and one of the available kernel modules and install, chances are you want the first
broadcom-wl-kmdl-2.6.18-194.17.4.el5 kernel modules for the Linux kernel package:
and not the centos.plus or xen ones.
Reboot, see your new interface detected, enter your credentials into the NetworkManager applet and be online wirelessly! The connection will probably be a bit slower than in Fedora 14.
I installed SL 5.5 a few weeks ago on this laptop to see how it would fare, but there seems to be no guide like this around, only half finished threads and recommendations to use ndiswrapper, which for some reason did not work for me. Setting this up in Fedora got me thinking and it wasn't more than a few minutes after that I had set it up in Scientific Linux as well.
Did others before figure this all out on their own? Going by some threads, not everybody did.
In SL/RHEL/CentOS 6 it shall be more straight forward, probably more like in recent Fedora releases (I hope).