How to modify the distance between branches when drawing trees using TiKZ?

Rather than setting this all manually, you can use tikz-qtree to construct these kinds of trees very easily, and it will adjust the sibling distance automatically. (I've enlarged the default sibling distance slightly; but no other manual changes are required.)

\documentclass{article}
\usepackage{tikz-qtree}
\begin{document}
 \tikzset{edge from parent/.style=
     {draw, edge from parent path={(\tikzparentnode) -- (\tikzchildnode)}}}
\begin{tikzpicture}[every tree node/.style={draw,circle},sibling distance=.25cm]
\matrix{
\Tree
 [.0 
    [.1 5 5 5 5  ] 
    [.2 ]
 ]
 &
 \Tree [.0 
    [.1 5 5 5 5 5 5 ] 
    [.2 6 6 ]
 ]
\\};
\end{tikzpicture}

\end{document}

You can change the sibling distance for each level of the tree individually, using level <number>/.style={sibling distance=<value>}:

\documentclass[a4paper,landscape]{scrartcl}
\usepackage{tikz}

\begin{document}
\begin{tikzpicture}[
    auto,
    level 1/.style={sibling distance=40mm},
    level 2/.style={sibling distance=10mm}]
    \node [circle,draw] (z){0}
        child {
            node[circle,draw] (a) {1}
            child { 
                node[circle,draw] (c) {5} 
            }
            child { 
                node[circle,draw] (d) {5} 
            }   
            child { 
                node[circle,draw] (e) {5} 
            }   
            child { 
                node[circle,draw] (f) {5} 
            }   
        }
        child {
            node[circle,draw] (b) {2}
        }
        ;
    \end{tikzpicture}
\end{document}