Ab initio calculations of the potential energy surface for the C-2(X-1 Sigma(+)(g)) + CH3CCH(X(1)A(1)) reaction have been carried at the G2M level of theory. The calculations show that the dicarbon molec.ule in the ground singlet electronic state can add to methylacetylene without a barrier producing a three-member or a four-member ring intermediate, which can rapidly rearrange to the most stable H3CCCCCH isomer on the C5H4 singlet surface. This isomer can then lose a hydrogen atom (H) or molecular hydrogen (H-2) from the CH3 group with the formation of H2CCCCCH and HCCCCCH, respectively. Alternatively, H atom migrations and three-member-ring closure/opening rearrangements followed by H and H-2 losses can lead to other isomers of the C5H3 and C5H2 species. According to the calculated energetics, the C-2(X-1 Sigma(+)(g)) + CH3CCH reaction is likely to be a major source of the C5H3 radicals (in particular, the most stable H2CCCCCH and HCCCHCCH isomers, which are relevant to the formation of benzene through the reactions with CH3). Among heavy-fragment product channels, only C3H3 + C2H and C-C3H2 + C2H2 might compete with C5H3 + H and C5H2 + H-2. RRKM calculations of reaction rate constants and product branching ratios depending on the reactive collision energy showed that the major reaction products are expected to be H2CCCCCH + H (64-66%) and HCCCHCCH + H (34-30%), with minor contributions from HCCCCCH + H2 (1-2%), HCCCHCC + H2 (UP to 1%), C3H3 + C2H (up to 1%), and C-C3H2 + C2H2 (up to 0.1%) if the energy randomization is complete. The calculations also indicate that the C2(X-1 Sigma(+)(g)) + CH3CCH(X(1)A(1)) reaction can proceed by direct H-abstraction of a methyl hydrogen to form C3H3 + C2H almost without a barrier.