The ground state spin-wave excitations and thermodynamic properties of two types of ferrimagnetic chains are investigated: the alternating spin-1/2 spin-5/2 chain and a similar chain with a spin-1/2 pendant attached to the spin-5/2 site. Results for magnetic susceptibility, magnetization and specific heat are obtained through the finite-temperature Lanczos method with the aim in describing available experimental data, as well as comparison with theoretical results from the semiclassical approximation and the low-temperature susceptibility expansion derived from Takahashis modified spin-wave theory. In particular, we study in detail the temperature vs. magnetic field phase diagram of the spin-1/2 spin-5/2 chain, in which several low-temperature quantum phases are identified: the Luttinger Liquid phase, the ferrimagnetic plateau and the fully polarized one, and the respective quantum critical points and crossover lines.