Two fully characterized specimens of pentatungsten trisilicide, nominally W5Si3, one believed to have been prepared by direct reaction of the elements in a sealed tube, and the other by are melting, have been studied by fluorine-combustion calorimetry. Chemical analyses of the samples played a pivotal role in this work, and their effects on the results are discussed in detail. The massic energies of combustion of the samples according to the reaction : W5Si3+x(cr) + (21 + 2x)F-2(g) = 5WF(6)(g) + (3 + x)SiF4(g), were measured calorimetrically. Results derived for the standard molar enthalpies of formation Delta(f)H(m)(o)(W5Si3+x) at temperature T = 298.15 K and standard pressure p(o) = 101.325 kPa are : -(126 +/- 18) kJ . mol(-1) for x = 0, and -(97 +/- 20) kJ . mol(-1) for x = 0.115. (Here, and throughout this paper, uncertainties are uncertainty intervals equal to twice the standard deviation of the mean.) The value for Delta(f)H(m)(o)(W5Si3,cr) agrees with estimates from Knudsen-effusion vaporization studies at elevated temperatures. There have been no previous reports of thermodynamic investigations of nonstoichiometric pentatungsten trisilicides.