Perceptron learning rule doesn't work
I think you're mixing up the weight vector $w$ and the actual hyperplane defining the decision boundary. The way to interpret $w$ is as a vector which is orthogonal to any vector lying on the hyperplane. See these slides for some visualization.

As you've said, the decision is defined by $1$ if $w_1 x + w_2 y &gt; 0$ and $0$ otherwise. So to find the actual hyperplane (decision boundary) we can just solve for the place where the decision changes, which is at $0$. Using your $w$ we have 
$$
\begin{align*}
w_1 x + w_2 y &amp;= 0\\
\implies 5 x + -5y &amp;= 0\\
\implies x &amp;= y.
\end{align*}
$$
So the decision boundary is given by the line $y = x$. Plotting this with your points we see that this $w$ does indeed define a separating hyperplane.