  Over the last decade it has become clear that discrete Painlev\'e equations
appear in a wide range of important mathematical and physical problems. Thus,
the question of recognizing a given non-autonomous recurrence as a discrete
Painlev\'e equation and determining its type according to Sakai's
classification scheme, understanding whether it is equivalent to some known
(model) example, and especially finding an explicit change of coordinates
transforming it to such an example, becomes one of the central ones.
Fortunately, Sakai's geometric theory provides an almost algorithmic procedure
for answering this question. In this paper we illustrate this procedure by
studying an example coming from the theory of discrete orthogonal polynomials.
There are many connections between orthogonal polynomials and Painlev\'e
equations, both differential and discrete. In particular, often the
coefficients of three-term recurrence relations for discrete orthogonal
polynomials can be expressed in terms of solutions of discrete Painlev\'e
equations. In this work we study discrete orthogonal polynomials with general
hypergeometric weight and show that their recurrence coefficients satisfy,
after some change of variables, the standard discrete Painlev\'e-V equation. We
also provide an explicit change of variables transforming this equation to the
standard form.
