  We review the construction of the mixed Painlev\'e P$_{III-V}$ system in
terms of a 4-boson integrable model and discuss its symmetries. Such a mixed
system consist of an hybrid differential equation that for special limits of
its parameters reduces to either Painlev\'e P$_{III}$ or P$_{V}$.
  The aim of this paper is to describe solutions of P$_{III-V}$ model. In
particular, we determine and classify rational, power series and transcendental
solutions of P$_{III-V}$. A class of power series solutions is shown to be
convergent in accordance with the Briot-Bouquet theorem. Moreover, the
P$_{III-V}$ equations are reduced to Riccati equations and solved for special
values of parameters. The corresponding Riccati solutions can be expressed as
Whittaker functions or alternatively confluent hypergeometric and Laguerre
functions and are given by ratios of polynomials of order $n$ when the
parameter of P$_{III-V}$ equation is quantized by integer $n \in \mathbb{Z}$.
