Clip, but add arrowheads to end of clipped curve

Clip, but add arrowheads to end of clipped curve

I have the following code:
\documentclass{article}
\usepackage{tikz}
\begin{document}
\begin{tikzpicture}
\clip (-5,-5) rectangle (5,5);
\draw[help lines] (-5,-5) grid (5,5);
\draw[->] (-5,0) -- (5,0) node[right] {$x$};
\draw[->] (0,-5) -- (0,5) node[above] {$y$};
\draw[<->,domain=-5:5,smooth,variable=\t]
plot (\t, {pow(\t,2)});
\end{tikzpicture}
\end{document}
Is it possible to add arrowheads to the ends of the parabola after it has
been clipped?