  We review Exoo's 1989 paper, which demonstrates that a lower bound for the
Ramsey number $R(5,5)$ is $43$. We provide an efficient way to verify the
claims in the paper, adding detailed proofs. In particular, we replace the
reference to computer verification by concise arguments. Using our
understanding of the insight behind these proofs, we are also able to analyse
variations of the graph constructions to obtain, for example, colourings of
$K_{43}$ which have very few monochromatic $K_5$.
