An efficient algorithmic solution to the classical five-point relative pose problem is presented. The problem is to find the possible solutions for relative camera motion between two calibrated views given five corresponding points. The algorithm consists of computing the coefficients of a tenth degree polynomial and subsequently finding its roots. It is the first algorithm well suited for numerical implementation that also corresponds to the inherent complexity of the problem. The algorithm is used in a robust hypothesise-and-test framework to estimate structure and motion in real-time.