You have taken the default install and the used LVM (See the install section on PArtitioning and disk druid.)
You must have installed a lot of extras otherwise there would be plenty of free space.
The fastest way would be to re-install and you may need even more space, 20 GB total.
About 15-16 for / and 2GB for swap, 320MB for /boot
This is how you extent the LV in a VG to another PV. see man lvm
create a partition out of the free space (sdan) with type 8e
# /dev/sdan (the 5 GB)
# vgextend VolGroup00 /dev/sdan (the 5GB)
lvextend /dev/VolGrouup00/LogVol00 /dev/sdan (the 5GB)