Put the entire tree in a \resizebox from the graphicx package. Here's what the graphics guide has to say about this command:
\resizebox{⟨h-length⟩}{⟨v-length⟩}{⟨text⟩}
Scale text so that the width is h-length. If ! is used as either
length argument, the other argument is used to determine a scale
factor that is used in both directions. Normally v-length refers to
the height of the box, but in the star form, it refers to the ‘height
+ depth’. As normal for LaTeX2ε box length arguments, \height, \width, \totalheight, \depth may be used to refer to the original size
of the box.
\bigskip, \newpage, \hfill, and \hspace{0pt} are just used to make the example spacing look nicer.
Note that in order for the vertical resizing to work, you need to put the \Tree in a tikzpicture environment.
And of course, you can also just use 5cm as a length; I only included lengths related to typesetting dimensions in my examples.
\documentclass[12pt]{article}
\usepackage[a6paper,showframe]{geometry}% just to demonstrate the effects
\usepackage{graphicx}
\usepackage{tikz-qtree}
\begin{document}
\setlength{\parindent}{0cm}% get rid of paragraph indents for this example
%
% HORIZONTAL RESIZING FOR WIDE TREES
%
Original Size:
\Tree[.Top A B C D E F G H I J K L M N O P ]
\bigskip
Full linewidth:
\resizebox{\linewidth}{!}{%
\Tree[.Top A B C D E F G H I J K L M N O P ]
}
\bigskip
Linewidth minus 1cm:
\resizebox{\dimexpr\linewidth-1cm}{!}{%
\Tree[.Top A B C D E F G H I J K L M N O P ]
}
\bigskip
Half linewidth:
\resizebox{.5\linewidth}{!}{%
\Tree[.Top A B C D E F G H I J K L M N O P ]
}
\bigskip
%
% VERTICAL RESIZING FOR TALL TREES
%
Page 2: original size
Page 3: textheight, textheight minus 1cm, half textheight
\newpage
\begin{tikzpicture}\Tree[.A [.B [.C [.D [.E [.F [.G [.H [.I [.J [.K [.L [.M [.N [.O [. P ]]]]]]]]]]]]]]]]\end{tikzpicture}
\newpage
\hfill
\resizebox{!}{\textheight}{\begin{tikzpicture}
\Tree[.A [.B [.C [.D [.E [.F [.G [.H [.I [.J [.K [.L [.M [.N [.O [. P ]]]]]]]]]]]]]]]]
\end{tikzpicture}}
\hfill
\resizebox{!}{\dimexpr\textheight-1cm}{\begin{tikzpicture}
\Tree[.A [.B [.C [.D [.E [.F [.G [.H [.I [.J [.K [.L [.M [.N [.O [. P ]]]]]]]]]]]]]]]]
\end{tikzpicture}}
\hfill
\resizebox{!}{.5\textheight}{\begin{tikzpicture}
\Tree[.A [.B [.C [.D [.E [.F [.G [.H [.I [.J [.K [.L [.M [.N [.O [. P ]]]]]]]]]]]]]]]]
\end{tikzpicture}}
\hfill\hspace{0pt}
\end{document}
