Fermionic approach to elementary excitations and magnetization plateaus in an <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>S</mml:mi> <mml:mo>=</mml:mo> <mml:mn>1</mml:mn> <mml:mo>/</mml:mo> <mml:mn>2</mml:mn> </mml:mr

We study the elementary excitations and magnetization of a one-dimensional spin-1/2 XX chain comprising trimer-dimer units (the J1-J1-J2-J3-J2 topology) under a transverse magnetic field h. Using Green's function theory and the Jordan-Wigner transformation, we map the system onto spinless fermions and focus on antiferromagnetic (AFM) interactions. At zero temperature, distinct 1/5 and 3/5 magnetization plateaus emerge, determined by the global periodicity Q=5, with the number of plateaus matching the number of excitation gaps above the Fermi level of the spinless fermions. The magnetic phase diagram in the (h-Js) plane features a Luttinger liquid (LL) state, a gapless AFM state, two magnetization plateau states, and a fully polarized gapped magnetic state. The widths of the LL and gapless AFM phases are found to be proportional to the bandwidths gamma = |E(k=0)-E(k=pi)| of the corresponding elementary excitations, whereas the widths of the magnetization plateau states are governed by the excitation gaps. Our study opens new directions for exploring interacting trimer-dimer spin chains in quantum magnetism using experimental techniques such as neutron scattering, as well as theoretical and numerical approaches including quantum Monte Carlo (QMC) and density-matrix renormalization group (DMRG) methods. Furthermore, we extend the Oshikawa-Yamanaka-Affleck (OYA) condition to generalized cluster chains, demonstrating that the allowed magnetization plateaus are governed by the global periodicity of the chain (e.g., Q=5 for a trimer-dimer chain), rather than by the local periodicity of individual units (Q=3 for a trimer or Q=2 for a dimer).