  We show that the Lagrange top with a linearly time-dependent moment of
inertia is equivalent to the degenerate fifth Painlev\'e equation. More
generally we show that the harmonic Lagrange top (the ordinary Lagrange top
with a quadratic term added in the potential) is equivalent to the fifth
Painlev\'e equation when the potential is made time-dependent in an appropriate
way. Through this identification two of the parameters of the fifth Painlev\'e
equation acquire the interpretation of global action variables. We discuss the
relation to the confluent Heun equation, which is the Schr\"odinger equation of
the Lagrange top, and discuss the dynamics of $P_V$ from the point of view of
the Lagrange top.
