Well the name used by Windows may say one thing and the driver is really something else.
Yes the latest is alsa does work well with the 2.6.20 kernel or newer. Both can be applied to FC5 by various means. Personally I prefer building my own kernels, but FC5 does have a 2.6.20 series built kernel available;
Maybe you need to do something like: yum update
The Fedora Core Development alsa rpm packages may work with Fedora Core 5 but I cannot say for sure. Get the list of the current alsa rpm packages by typing something like;
/bin/rpm -qa 'alsa*'
Down the newer development rpm versions and test install; /bin/rpm -uvh alsa*.rpm --test
if you get no errors then remove the --test switch and really install.