This thesis in algorithmic number theory presents a new probabilistic algorithm for solving dimension 5 quadratic equations over Z or Q without using any factorisation. It has a much better complexity than existing algorithms and is based on two other algorithms : one from Simon and the other from Pollard and Schnorr. After a survey on the theory of quadratic forms, we explain how this algorithm works. What follows is a detailed analysis of the complexity of the algorithm for which we will use an effective version of the Tchebotarev density theorem.
