Given that you have a clean installation of CentOS 7 which was already updated, by you, then you still have some dependencies to install make and install the external Zsh from the source. You must be root to get the stuff done.
yum groupinstall "Development tools"
gcc -v
yum install ncurses-devel
wget https://sourceforge.net/projects/zsh/files/zsh/5.6.2/zsh-5.6.2.tar.xz/download
tar -xvJf download
cd zsh-5.6.2
./configure
make
make install
vi /etc/shells
/usr/local/bin/zsh
chsh -s /usr/local/bin/zsh
Thanks alot, this works, a little tip: when download zsh replace the version number with the newest version :)