In several places I have come across references to a 2005-6 preprint of Denis Simon entitled
Quadratic equations in dimensions 4, 5, and more
This paper gives fast algorithms to find isotropic vectors in a 4 or 5 dimensional quadratic space over $\mathbb{Q}$, based on indefinite LLL.
I have been unable to get a hold of it. Is it online? Has it been published?