Formation of Ta5Si3 by self-propagating high-temperature synthesis (SHS) from elemental powder compacts of Ta:Si = 5:3 was experimentally and numerically studied. Experimental evidence showed that the increase of either sample density or preheating temperature led to the increase of combustion wave velocity and reaction temperature. The apparent activation energy, Ea ≈ 108 kJ/mol, was determined for the synthesis reaction. Based upon numerical simulation, the Arrhenius factor of the rate function, K0 = 2.5 × 107 s−1, was obtained for the 5Ta + 3Si combustion system. In addition, the influence of sample density on combustion wave kinetics was correlated with the effective thermal conductivity (keff) of the powder compact. By adopting 0.005 ≤ keff/kbulk ≤ 0.016 in the computation model, the calculated combustion velocity and temperature were in good agreement with experimental data of the samples with compaction densities between 35% and 45% theoretical maximum density (TMD).