  A birational transformation is one which leaves invariant an ordinary
differential equation, only changing its parameters. We first recall the
consistent truncation which has allowed us to obtain the first degree
birational transformation of Okamoto for the master Painlev\'e equation P6.
Then we improve it by adding a preliminary step, which is to find all the
Riccati subequations of the considered Pn before performing the truncation. We
discuss in some detail the main novelties of our method, taking as an example
the simplest Painlev\'e equation for that purpose, P2. Finally, we apply the
method to P5 and obtain its two inequivalent first degree birational
transformations.
