Sp(4) gauge theory with two fundamental and three antisymmetric fermion flavours is a template for beyond the standard model strong interactions that can give rise to a composite Higgs boson through the breaking of the global fundamental flavour symmetry and at the same time to a partial composite top quark state that explains why the observed mass of the latter particle is at the electroweak scale. Partial top compositeness results from the mixing of the standard model top quark with a chimera baryon, i.e. a baryonic state formed with two quarks in the fundamental and one quark in the antisymmetric representation. A necessary ingredient for partial top compositeness is the generation of a large anomalous dimension for the chimera baryon. Lattice gauge theory can be used as a framework to study non-perturbatively these phenomena, in order to verify their viability beyond semi-quantitative arguments. After a brief review of the relevant analytic considerations, in this talk, I will discuss our recent numerical calculations for the target Sp(4) model, presenting results for the meson spectrum and for the chimera baryon.