Hi, alettames!
The Cent OS 5 is way too old to run synfigstudio packages provided by synfig.org. To run it you need version of glib2 >= 2.18.4 ( a version including ‘libgio*’ ). The version provided with Cent OS 5 is 2.12.3.
I would recommend to use some newer linux distribution, like CentOS 6, Fedora or Ubuntu - you will get much better linux experience. 
If you still decide to stick with CentOS 5, you can try to install new version of glib2 manually. Just issue following commands as root user:
[code]# yum install gettext-devel
wget http://ftp.acc.umu.se/pub/GNOME/sources/glib/2.18/glib-2.18.4.tar.gz
mkdir /usr/local/glib218
tar xvf glib-2.18.4.tar.gz
cd glib-2.18.4/
./configure --prefix=/usr/local/glib218/
make
make install[/code]
After that, everytime you want to run synfigstudio you will need to issue following commands as normal user:
$ export LD_LIBRARY_PATH=/usr/local/glib218/lib
$ synfigstudio