[Tex/LaTex] Drawing a C_5 graph with colored vertices

Question

How can I make the following graph a simple graph with these colors?

$\begin{tikzpicture}[shorten >=0.5pt,node distance=2.2cm,on grid,auto, vertex/.style={circle, draw, minimum size=0.001cm}] 


\node[vertex, fill=blue] (x) {};
\node[vertex, fill=red] (y) [right=of x] {}; 
\node[vertex, fill=yellow] (z) [below=of y] {}; 
\node[vertex, fill=green] (u) [below=of x] {};
\node[vertex, fill=green] (a) [right=of y] {};


\path[-] (x) edge [bend left=40]  node {} (y);
\path[-] (y) edge [bend left=40] node {} (a);
\path[-] (a) edge [bend left=40] node {} (z); 
\path[-] (x) edge [bend right=40] node {} (u);
\path[-] (z) edge  [bend left=40] node {} (u);


\end{tikzpicture}$

Answer 1

Most likely I do not understand the question. Here is a code which produces a Cayley graph with the same colors as your code.

\documentclass[border=3.14mm,tikz]{standalone}
\begin{document}
\begin{tikzpicture}[vertex/.style={circle, draw}] 
\foreach \X[count=\Y] in {blue,red,green,yellow,green}
{\node[vertex, fill=\X] (x-\Y) at ({72*\Y+30}:2){}; }
\foreach \X[count=\Y] in {0,...,4}
{\ifnum\X=0
\draw (x-\Y) -- (x-5);
\else
\draw (x-\Y) -- (x-\X);
\fi}
\end{tikzpicture}
\end{document}

I saw that you bent some edges. If you really want to do that, then you may want to consider this snippet.

\documentclass[border=3.14mm,tikz]{standalone}
\begin{document}
\begin{tikzpicture}[vertex/.style={circle, draw}] 
\foreach \X[count=\Y] in {blue,red,green,yellow,green}
{\node[vertex, fill=\X] (x-\Y) at ({72*\Y+30}:2){}; }
\foreach \X[count=\Y] in {0,...,4}
{\ifnum\X=0
\path[-] (x-\Y) edge [bend left=30](x-5);
\else
\path[-] (x-\Y) edge [bend left=30](x-\X);
\fi}
\end{tikzpicture}
\end{document}