Systems of Differential Equations · Hard problem

Let $A=\begin{pmatrix}1&5\\-1&-1\end{pmatrix}$ and $\mathbf x'=A\mathbf x$ with $\mathbf x(0)=(1,0)$. The orbit is an ellipse around the origin (the eigenvalues are purely imaginary, but $A$ is not a pure rotation). Find the smallest value that $x(t)$ ever takes.